@incollection{statphys23_1037,
        title = {A Stochastic Process with a Size-Dependent Standard Deviation 
 for Growth Rates},
        address = {Genova, Italy},
        author = {B.P. Boris Podobnik and H.E. Stanley and I.G. Grosse},
        booktitle = {Abstract Book of the XXIII IUPAP International Conference on Statistical Physics},
        editor = {Luciano Pietronero and Vittorio Loreto and Stefano Zapperi},
        month = {9-13 July},
        year = 2007,
        url = {http://st23.statphys23.org/webservices/abstract/preview_pop.php?ID_PAPER=1037},
        abstract = {Stationary and nonstationary stochastic processes [P. Jung, {\it Rev. Mod.
Phys.} {\bf 234}, 175 (1993)] occur in a variety of phenomena as different
as Brownian motion [A. Einstein, {\it Ann. Phys.} {\bf 17}, 549 (1905)],
Johnson noise [J. Johnson, {\it Phys. Rev.} {\bf 32}, 97 (1928)], stellar
dynamics [S. Chandrasekhar, {\it Rev. Mod. Phys.} {\bf 15}, 1 (1943)], and
quantum optics [H. Risken, in {\it Progress in Optics}.

Besides in physics, stochastic processes have been successfully applied in
economics for modeling and thus explaining diverse levels of economics
systems, ranging from the ``micro'' level of company products to the
``macro'' level of company sizes and even national economies.  Recently, Fu
et al.\ [D. Fu et al., {\it Proc. Natl. Acad. Sci. USA\/} {\bf 102}, 18801
(2005)] show that for different economic variables from both the micro and
the macro level, the distribution of logarithmic growth rates are
approximately (i) exponential in the central part, (ii) power-law decaying
in the tails, and that there is (iii) a monotonically decreasing power-law
relation between the company sales and the standard deviation of logarithmic
growth rates.

Fu et al.\ propose a process recently cited in the Handbook of Industrial
Organization [Volume 3, edited by Robert Porter and Mark Armstrong] for
modeling the empirical observations (i) and (ii), but this model fails to
reproduce observation (iii). 

For modeling observations (i)--(iii), we propose the multiplicative 
stochastic process of logarithmic growth rates
\begin{equation}
R_t \equiv \ln\left({S_t\over S_{t-1}}\right)=\mu_0\Delta t +
(S_{t-1})^\gamma\sigma_0\eta_t\Delta t,
\end{equation}
where $\sigma$, $\gamma$, and $\mu$ are three parameters, $\eta_t$ is an
i.i.d.\ Gaussian noise, and $S_t $ is the random variable. 

When the parameter $\gamma$ introduced for modeling the dependence of the
standard deviation $\sigma(R_t)$ on the size $S_t$ is set equal to zero, the
stochastic process reduces to geometric Brownian motion, the most
widely employed stochastic process in finance. The process can
also be related to the Ornstein-Uhlenbeck process, a well-known stochastic
process introduced in physics.

For different time series of logarithmic growth rates $R_{t}$ with
$\gamma=-0.15$, we calculate the average size $\langle S \rangle$ and the
standard deviation $\sigma(R_t)$.  Fig.~1(a) shows that, due to $\gamma < 0$,
$\sigma(R_t)$ versus $\langle S\rangle$ scales as a power law $\sigma(R_t)
\propto \langle S\rangle^{\beta}$, where $\beta=\gamma$.

We find in Fig.~1(b) that for $\gamma=-0.15$ the central part of
distribution $P(R_t|S_0)$ can be approximated by an exponential
distribution, and Fig.~1(c) shows that the far tails of $P(R_t|S_0)$ can be
approximated by power-laws, where the parameter $\sigma$ controls the
power-law exponent. 

We also find in Fig.~1(d) that four important macroeconomic
variables, (export, import, debt, and investments) exhibit the same
properties (i)-(iii).},
	biburl = {http://www.bibsonomy.org/bibtex/226d733662118f1784c159e846f6552d5/statphys23},
	keywords = {series time walks modeling random topic-11 statphys23 econophysics analysis stochastic}
}

@incollection{statphys23_0973,
        title = {Conditioning of data outliers to identify and obtain the scaling behaviour of statistically self-similar and multifractal, non-Gaussian processes from finite length time-series},
        address = {Genova, Italy},
        author = {K. Kiyani and S.C. Chapman and B. Hnat},
        booktitle = {Abstract Book of the XXIII IUPAP International Conference on Statistical Physics},
        editor = {Luciano Pietronero and Vittorio Loreto and Stefano Zapperi},
        month = {9-13 July},
        year = 2007,
        url = {http://st23.statphys23.org/webservices/abstract/preview_pop.php?ID_PAPER=973},
        abstract = {We address the generic problem of extracting the scaling exponents of a stationary non-Gaussian process realised by a time-series of finite length, where information about the process is not known \emph{a priori}. Estimating the scaling exponents relies upon estimating the moments, or more typically structure functions, of the probability density of the differenced time-series. If the probability density is heavy tailed, outliers strongly influence the scaling behaviour of the moments. From an operational point of view, we wish to recover the scaling exponents of the underlying process by excluding a minimal population of the outliers. This method is particularly sensitive in distinguishing and quantifying self-affine, or self-similar, scaling from weak multifractality. We will illustrate this with two synthetically generated reference models: the first of which is manifestly self-similar, an $\alpha$-stable Levy process; and the second, manifestly multifractal, a cascade \emph{p}-model. We show that for the symmetric $\alpha$-stable Levy process, the Levy exponent is recovered in up to the 6th order moment after only ~0.1-0.5 percent of the data are excluded. The scaling properties of the excluded outliers can also be tested to provide additional information about the system. Unlike the self-similar Levy process, which shows a convergence of all its exponents for each moment order, the multifractal \emph{p}-model process shows a divergence of its exponents as the outlying data points are excluded. Importantly then, successively removing outlying data points does not convert the multifractal \emph{p}-model time-series into a self-similar process. Although this is expected for a multifractal, as the Hurst exponent is locally dependent on the position in the time-series, we will show that outliers distort the scaling of these processes too and that conditioning is also needed. We will be discussing a way of distinguishing this multifractal scaling thus presenting a unified treatment of the handling and remedying of extreme data outliers.

As a practical application of the above technique we quantify the scaling of magnetic energy density in the inertial range of solar wind turbulence seen in situ at 1 AU with respect to solar activity. At solar maximum, when the coronal magnetic field is dynamic and topologically complex, we find self-similar scaling in the solar wind, whereas at solar minimum, when the coronal fields are more ordered, we find multifractality. We propose that the self-similar scaling seen at solar maximum is indicative of the non-trivial evolution of the early stages of the development of turbulence being represented near 1 AU in the elliptic at solar maximum, and thus reflects the fractal structure of the processes which drive the interplanetary solar wind at its solar origin. More importantly, this quantifies the solar wind signature that is of direct coronal origin, and distinguishes it from that of local MHD turbulence, with quantitative implications for our understanding of coronal heating of the solar wind. 

[1] K. Kiyani, S. C. Chapman and B. Hnat , Phys. Rev. E 74(5), 047611 (2006)

[2] B. Hnat, S. C. Chapman, G. Rowlands, N. W. Watkins, and W. M. Farrell, Geophys. Res. Lett. 29 (2002)

[3] K. Kiyani, S. C. Chapman, B. Hnat, R. M. Nicol, (2007)http://arxiv.org/abs/physics/0702123},
	biburl = {http://www.bibsonomy.org/bibtex/2bfb8741e77da75c0673ea00800d27407/statphys23},
	keywords = {processes series time topic-11 statphys23 turbulence fractal analysis levy scaling}
}

@incollection{statphys23_0969,
        title = {Trade-off between information and variability in time series analysis},
        address = {Genova, Italy},
        author = {R. Hernandez-perez and L. Guzman-vargas and F. Angulo Brown},
        booktitle = {Abstract Book of the XXIII IUPAP International Conference on Statistical Physics},
        editor = {Luciano Pietronero and Vittorio Loreto and Stefano Zapperi},
        month = {9-13 July},
        year = 2007,
        url = {http://st23.statphys23.org/webservices/abstract/preview_pop.php?ID_PAPER=969},
        abstract = {We present numerical evidence of the presence of a trade-off between the amount of information comprised in a time series, which is the output of a natural system, and the entropy produced by the system in generating this information. In particular, we analyze the relation between the spectral correlation exponent and the entropy. We observed that, as the time correlations increase,
 the variability of the signal reduces. Finally, we discuss a hypothesis on how this trade-off could be related to energy optimization done by the system, while at the same increasing its robustness on the information generation.},
	biburl = {http://www.bibsonomy.org/bibtex/247054b93d1caf1e1319462056fbaff3a/statphys23},
	keywords = {series time entropy topic-11 statphys23}
}

@incollection{statphys23_0888,
        title = {Generic statistical distribution in finances and human and ecological communities},
        address = {Genova, Italy},
        author = {G. Cocho and R. Mansilla and G. Martinez-mekler},
        booktitle = {Abstract Book of the XXIII IUPAP International Conference on Statistical Physics},
        editor = {Luciano Pietronero and Vittorio Loreto and Stefano Zapperi},
        month = {9-13 July},
        year = 2007,
        url = {http://st23.statphys23.org/webservices/abstract/preview_pop.php?ID_PAPER=888},
        abstract = {Central limit theorems show that a collection of stochastic processes follow a reduced class of probability distributions. Such is the case for statistically independent variables leading to Gausssian and Levy distributions. On the other hand, the case of strongly correlated variables such as fluctuations in phase transitions give a power law behavior.  We have found a ubiquitous distribution for population-rank data given by: $f(r)=Ae^{-dr}(N+1-r)^{b}/r^{a}$, where $r$ is the rank, $N$ the maximum value of $r$, $A$ a normalization factor and $a,b,d$ are parameters. In most of the cases we have found that d is close to zero. Here we show that a master equation, which generalizes Hubbell's death and birth ecological community approach [1,2], has as limiting probability distribution the above expression. We show that this distribution fits remarkably well ecological community and urban population data. In both cases the master equation suggests underlying population migration behaviors. The distribution also shows excellent agreement with financial time series data. However for this case the validity of our equations remains unclear.

1) Hubbell, D.P., A unified theory of biogeography and relative species abundance and its applications to tropical rain forests and coral reefs, Coral Reefs, volume 16, S9-S21 (1997).\\
2) Volkov, I., Banavar J.R., Hubbell, S.P. and Maritan A, Neutral theory and relative species abundance in ecology, Nature, volume 424, 2035-1037 (2003).},
	biburl = {http://www.bibsonomy.org/bibtex/2d6bfa0d91ea39e6cf98dd3e37b74540a/statphys23},
	keywords = {financial functions series communities ecological rank-size topic-11 distributions master urban time equation ditribution statphys23 population}
}

@incollection{statphys23_0763,
        title = {Critical exponents and amplitude ratios of the three dimensional XY universality class},
        address = {Genova, Italy},
        author = {M. Campostrini and M. Hasenbusch and A. Pelissetto and E. Vicari},
        booktitle = {Abstract Book of the XXIII IUPAP International Conference on Statistical Physics},
        editor = {Luciano Pietronero and Vittorio Loreto and Stefano Zapperi},
        month = {9-13 July},
        year = 2007,
        url = {http://st23.statphys23.org/webservices/abstract/preview_pop.php?ID_PAPER=763},
        abstract = {We improve the theoretical estimates of the critical exponents for the
three-dimensional XY universality class, which apply to the superfluid
transition in $^4$He along the $\lambda$-line $T_\lambda(P)$ of its
phase diagram. We obtain the estimates $\alpha=-0.0151(3)$,
$\nu=0.6717(1)$, $\eta=0.0381(2)$, $\gamma=1.3178(2)$,
$\beta=0.3486(1)$, and $\delta=4.780(1)$.  These results are obtained by
a finite-size scaling analyses of high-statistics Monte Carlo
simulations up to lattice size $L=128$ and resummations of 22nd order
high-temperature expansions of two lattice models with suppressed
leading scaling corrections.  We note that our result for the
specific-heat exponent $\alpha$ disagrees with the most recent
experimental estimate $\alpha=-0.0127(3)$ at the superfluid transition
of $^4$He in microgravity environment.

Furthermore,
we have simulated one of the two models
in the low and the high temperature phase for reduced
temperatures down to $|T-T_c|/T_c \approx 0.0017$ on lattices of a size up to
$350^3$. Our results for the internal energy and the specific heat,
combined with our accurate estimate of $T_c$ and data for the
internal energy and the specific heat at $T_c$, lead to the estimate
$R_{\alpha} = (1-A_+/A_-)/\alpha = 4.01(5)$, where
$A_{\pm}$ is the amplitude of the specific
heat in the high and the low temperature phase, respectively. Also here,
the most recent experimental result $R_{\alpha} = 4.154(22)$ is not fully
consistent with our value.},
	biburl = {http://www.bibsonomy.org/bibtex/2e7c2d7587e739d93ccb8c3ed2a90534e/statphys23},
	keywords = {lambda-transition series lattice class universality simulation xy temperature models improved topic-2 high montecarlo statphys23}
}

@incollection{statphys23_0657,
        title = {Critical behaviour of the contact process in heterogeneous and weakly-disordered systems},
        address = {Genova, Italy},
        author = {C.J. Neugebauer and S.V. Fallert and S.N. Taraskin},
        booktitle = {Abstract Book of the XXIII IUPAP International Conference on Statistical Physics},
        editor = {Luciano Pietronero and Vittorio Loreto and Stefano Zapperi},
        month = {9-13 July},
        year = 2007,
        url = {http://st23.statphys23.org/webservices/abstract/preview_pop.php?ID_PAPER=657},
        abstract = {While according to the Harris criterion the introduction of quenched disorder
is a relevant perturbation to the 
Directed Percolation (DP) universality class, which is amongst the most
common in nonequilibrium statistical mechanics, it is not clear
how exactly disorder changes the universal properties. 
The contact process (CP), a simple model for the spatial
spread of epidemics, is one of the DP class' archetypical models.
We have studied the one-dimensional CP in heterogeneous periodic 
and weakly-disordered environments using the supercritical series expansion
and Monte Carlo simulations. 
Heterogeneity was incorporated by introducing two different recovery rates. Phase-separation lines between active and absorbing states and critical
exponents $\beta$ have been calculated by analyzing the critical properties of
the perturbation series using two
methods, \emph{Nested Pad\'e Approximants} as well as \emph{Partial
  Differential Approximants}. A general analytical
expression for the locus of critical points is suggested
for the weak-disorder limit and confirmed
by the series expansion analysis and the MC simulations.
Our results for the critical exponents show that the CP in heterogeneous
environments remains in the %directed percolation (DP)
DP universality class, while for environments with quenched disorder, the data are compatible with the scenario of continuously changing critical exponents 
(see C.J.~Neugebauer et al., \emph{Phys. Rev. E} \textbf{74}, 040101(R) (2006), for more detail).},
	biburl = {http://www.bibsonomy.org/bibtex/2aebf518748663ba4c5d8f20680ae70b7/statphys23},
	keywords = {process series nonequilibrium expansion disorder topic-3 directed transition percolation statphys23 phase contact}
}

@incollection{statphys23_0641,
        title = {Multivariate Phase Rectified Signal Averaging},
        address = {Genova, Italy},
        author = {A.Y. Schumann and J.W. Kantelhardt and A. Bauer and G. Schmidt},
        booktitle = {Abstract Book of the XXIII IUPAP International Conference on Statistical Physics},
        editor = {Luciano Pietronero and Vittorio Loreto and Stefano Zapperi},
        month = {9-13 July},
        year = 2007,
        url = {http://st23.statphys23.org/webservices/abstract/preview_pop.php?ID_PAPER=641},
        abstract = {The behaviour of many natural complex systems is characterized by
nonstationarities and phase shifts making a conventional analysis of
periodicities not fully reliable. Recently, the method of Phase
Rectified Signal Averaging (PRSA) [1] has been introduced for the
extraction of non-stationary oscillations out of noisy signals with
varying mean. As an example, PRSA was shown to be superior in risk
classification of sudden cardiac death after initial myocardial
infarction [2]. The main advantage of the PRSA is its capability to
analyze separately periodicities occurring around increases (or,
alternatively, decreases) of the signal. We now suggest a multivariate
form of PRSA to study the relationships (i.e., interactions, partial
syncronization, etc.) between two or more complex signals. We compare
this method with cross correlation and cross spectra techniques and also
discuss the application of multivariate PRSA in a recent baroreflex
regulation study.


1) A. Bauer et al., Physica A 364, 423 (2006)\\
2) A. Bauer et al., The Lancet 367, 1674 (2006)},
	biburl = {http://www.bibsonomy.org/bibtex/265675c976623270a0e654462016a480c/statphys23},
	keywords = {systems series time system complex topic-10 quasi-periodicities cardiovascular statphys23 non-stationarities analysis}
}

@incollection{statphys23_0540,
        title = {Memory effects in Extreme Times of volatility process},
        address = {Genova, Italy},
        author = {J. Perello and J. Masoliver},
        booktitle = {Abstract Book of the XXIII IUPAP International Conference on Statistical Physics},
        editor = {Luciano Pietronero and Vittorio Loreto and Stefano Zapperi},
        month = {9-13 July},
        year = 2007,
        url = {http://st23.statphys23.org/webservices/abstract/preview_pop.php?ID_PAPER=540},
        abstract = {Extreme times techniques, generally applied to non-equilibrium statistical mechanical processes, are also useful for a better understanding of financial markets. We present a detailed study on the mean first-passage time for the volatility of return time series. The empirical results extracted from daily data of major indices seem to follow the same law regardless the kind of index thus suggesting an universal pattern. The empirical mean first-passage time to a certain level $L$ is fairly different from that of the Wiener process showing a dissimilar behavior depending on whether $L$ is higher or lower than the average volatility. All of this indicates a more complex dynamics in which a reverting force drives volatility toward its mean value. We thus present the mean first-passage time expressions of the most common stochastic volatility models whose approach is comparable to the random diffusion description. We discuss asymptotic approximations and confront them to empirical results with a good agreement with the ExpOU model.},
	biburl = {http://www.bibsonomy.org/bibtex/295eb49c512e2c145a22e5b467a96eec8/statphys23},
	keywords = {financial series diffusion scales random topic-11 first-passage stochastic volatility models time mean statphys23 multiple}
}

@incollection{statphys23_0444,
        title = {Statistics of the Extreme Values in Presence of Intermediate-Term Correlations},
        address = {Genova, Italy},
        author = {C. Pennetta},
        booktitle = {Abstract Book of the XXIII IUPAP International Conference on Statistical Physics},
        editor = {Luciano Pietronero and Vittorio Loreto and Stefano Zapperi},
        month = {9-13 July},
        year = 2007,
        url = {http://st23.statphys23.org/webservices/abstract/preview_pop.php?ID_PAPER=444},
        abstract = {The return time statistics (RTS) of the extreme values in time series with long-term correlations has been recently studied by Bunde et al. [1] and Altmann and Kantz [2]. These authors found that the return intervals of the extreme values follow a stretched exponential distribution with a value of the distribution exponent practically coincident with the correlation exponent of the time series. In this talk, the RTS of time series characterized by finite-term correlations with non-exponential decay will be considered. Precisely, the results will be discussed of numerical analyses of the return intervals of extreme values associated with the resistance fluctuations displayed by a resistor in a nonequilibrium stationary states [3]. These results show that when the auto-correlation function displays a non-exponential and non-power-law decay, the distribution of the return times of extreme values still keeps the stretched exponential form, with an exponent largely independent of the threshold [3]. Thus, the stretched exponential distribution cannot be considered an exclusive feature of long-term correlated time series. 


1) A. Bunde et al., {\em Physica A}, {\bf 330}, 1 (2003) and A. Bunde et al., {\em Phys. Rev. Lett.}, {\bf 94}, 048701 (2005). \\
2) E. G. Altmann, H. Kantz, {\em Phys. Rev.} E, {\bf 71}, 056106 (2005). \\
3) C. Pennetta, {\em Eur. Phys. J.} B, {\bf 50}, 95 (2006).},
	biburl = {http://www.bibsonomy.org/bibtex/2004f9734df8daadc2c24d473c1c7c880/statphys23},
	keywords = {processes series time phenomena extreme values topic-11 statphys23 analysis stochastic fluctuation}
}

@incollection{statphys23_0389,
        title = {A sum rule approach to detect complex correlation in time series},
        address = {Genova, Italy},
        author = {V. Alfi and A. Petri and L. Pietronero},
        booktitle = {Abstract Book of the XXIII IUPAP International Conference on Statistical Physics},
        editor = {Luciano Pietronero and Vittorio Loreto and Stefano Zapperi},
        month = {9-13 July},
        year = 2007,
        url = {http://st23.statphys23.org/webservices/abstract/preview_pop.php?ID_PAPER=389},
        abstract = {A basic problem in the analysis of time series consists in unveiling and 
characterizing correlations among the variables at different times. 
In practice inmost cases this consists in considering the two point 
correlations over a long time series. Often complex properties are related 
to the long time behavior of these correlations. 
However, in many systems, like for example financial time series, simple 
correlations are intrinsically excluded by the arbitrage hypothesis. 
This leaves space for subtle complex correlations which are clearly 
difficult to detect. 
The usual approach is to focus on the pair correlations for 
grouped variables like in the problem of volatility clustering. 
Also in this case the availability of long time series is fundamental. 
This poses another problem because the stationarity hypothesis is not 
always appropriate.
Inspired by these problems we introduce a new method to detect complex 
correlations in time series of finite size. 
The method comes from the Spitzerกวs identity which controls 
the extremal values for sums of random variables. 
The basic idea is that a deviation from this identity is a sign of 
correlations in the variables and it corresponds to a sort of sum 
rule for correlations of any extension also in non stationary processes.  
We have tested the method which has only four point correlations. 
The application to real financial data shows that the method is a practical 
tool to detect correlations of any type even in finite time series.
This is usually not possible with the standard statistical tools.},
	biburl = {http://www.bibsonomy.org/bibtex/2ae381688ccf551cedf24836c2128028d/statphys23},
	keywords = {systems financial series time complex social topic-11 statphys23 analysis economic statistical}
}

@incollection{statphys23_0354,
        title = {Spin-glass phase characterization by time-series analysis},
        address = {Genova, Italy},
        author = {E.E. Vogel and B. Fierro and F. Bachmann and G. Saravia},
        booktitle = {Abstract Book of the XXIII IUPAP International Conference on Statistical Physics},
        editor = {Luciano Pietronero and Vittorio Loreto and Stefano Zapperi},
        month = {9-13 July},
        year = 2007,
        url = {http://st23.statphys23.org/webservices/abstract/preview_pop.php?ID_PAPER=354},
        abstract = {We consider the usual two-dimensional Edwards-Anderson model for spin glasses, with mixed concentration of ferromagnetic (F) bonds and antiferromagnetic (A) bonds of the same magnitude. Concentrations of A bonds are varied in the interval [0.00, 0.11], where a spin-glass phase has been characterized by means of the Binder cumulant technique. Many random samples are prepared for each different sample size and for each concentration to allow a basic statistic analysis. For each sample a single spin-flip Monte Carlo process is performed at different temperatures, recording the evolution of the Edwards-Anderson parameter q. Each one of these runs is stored in a separate file for subsequent studies. Thus, for instance, the time autocorrelation function is found for each of these numeric experiments. Functions corresponding to different sizes cross as a funtion of temperature in a way similar to Binder cumulants also leading to phase characterizations. The line separating a ferromagnetic phase from a spin-glass phase obtained by the new method is reported. On the other hand, size of the compressed stored filed maximize at the critical temperature, for reasons not yet understood.},
	biburl = {http://www.bibsonomy.org/bibtex/2a226294d7e5617a00fa04a0b5408b4f8/statphys23},
	keywords = {series binder time glass data topic-9 spin statphys23 compression cumulant}
}

@incollection{statphys23_0112,
        title = {Estimation of Drift and Diffusion function in presence of measurement noise},
        address = {Genova, Italy},
        author = {D. Kleinhans and R. Friedrich},
        booktitle = {Abstract Book of the XXIII IUPAP International Conference on Statistical Physics},
        editor = {Luciano Pietronero and Vittorio Loreto and Stefano Zapperi},
        month = {9-13 July},
        year = 2007,
        url = {http://st23.statphys23.org/webservices/abstract/preview_pop.php?ID_PAPER=112},
        abstract = {The understanding of complex systems greatly has benefited from the
concept of order parameters, that obey stochastic partial differential
equations [1]. Recently, a method for the direct
estimation of these equation from measured data sets has been proposed
[2]. However, this procedure involves the estimation of
the moments of the transition probability density functions (pdfs) in
the limit of infinitesimal small increments in time, that frequently
are not accessible from discrete measurements. Moreover, measurement
noise seriously impacts the transition pdfs at small time increments
and, therefore, tampers the results of the estimation procedure.

This contribution addresses the progress of two recent works with
respect to this shortcoming. First, an iterative method was proposed,
that avoids the limiting procedure and, therefore, is less sensitive
to measurement noise [3]. It is based on the iterative
optimisation of the transition pdfs in reference to the pdfs, that
directly can be obtained form the measured data set. Recently, the
conformance of this procedure with maximum likelihood methods could be
demonstrated [4].

Second, the former method could be extended for noisy data
[5]. Thereby, the increasing impacts of measurement
noise on the transition pdfs at small time increments can be utilised
for the simultaneous estimation of the noise amplitude and the
process' dynamics. For the Ornstein-Uhlenbeck process, closed
expressions for the estimation procedure could be derived, that permit
the proper reconstruction even in case of high noise amplitudes.\\


1) H.~Haken.  \newblock {\em Synergetics}.
  \newblock Springer Series in Synergetics. Springer-Verlag, Berlin,
  2004.  \newblock Introduction and advanced topics, Reprint of the
  third (1983) edition [{\it Synergetics}] and the first (1983)
  edition [{\it Advanced synergetics}].\\
2) S.~Siegert, R.~Friedrich, and J.~Peinke.
  \newblock Analysis of datasets of stochastic systems.  \newblock
  {\em Physics Letters A}, 243:275--280, 1998.\\
3) D.~Kleinhans, R.~Friedrich, A.~Nawroth, and
  J.~Peinke.  \newblock An iterative procedure for the estimation of
  drift and diffusion coefficients of langevin processes.  \newblock
  {\em Phys Lett A}, 346:42--46, 2005.\\
4) D.~Kleinhans and R.~Friedrich.  \newblock
  Maximum likelihood estimation of drift and diffusion functions.
  \newblock {\em (to be published in Phys. Lett.  A)}, preprint
  available at http://arxiv.org/abs/physics/0611102.\\
5) F.~Boettcher, J.~Peinke, D.~Kleinhans,
  R.~Friedrich, P.G.~Lind, and M.~Haase.  \newblock Reconstruction
  of complex dynamical systems affected by strong measurement noise.
  \newblock {\em Phys. Rev. Lett.}, 97:090603, 2006.},
	biburl = {http://www.bibsonomy.org/bibtex/209bf4c5ca4ef99ca3248ae0688f2e882/statphys23},
	keywords = {processes series time topic-5 statphys23 analysis stochastic noise measurement}
}

@incollection{statphys23_0086,
        title = {Microscopic dynamics of ion motion in microplasmas from nonlinear time-series analysis.},
        address = {Genova, Italy},
        author = {M. Romero-Bastida and M.A. Olivares-robles},
        booktitle = {Abstract Book of the XXIII IUPAP International Conference on Statistical Physics},
        editor = {Luciano Pietronero and Vittorio Loreto and Stefano Zapperi},
        month = {9-13 July},
        year = 2007,
        url = {http://st23.statphys23.org/webservices/abstract/preview_pop.php?ID_PAPER=86},
        abstract = {The problem of characterizing the dynamical regime, either regular or chaotic, of a Hamiltonian many-degrees-of-freedom system is investigated by analyzing the computer simulated position and velocity time series of ions confined in a Penning trap and forming so-called microplasmas. The ($\varepsilon,\tau$) entropy, which measures the amount of information generated by unit time at different scales $\tau$ of time and $\varepsilon$ of the observable, is numerically computed by methods of nonlinear time-series analysis using the position and velocity signals of a single ion for different trap geometries, as well as for various values of both the energy of the system and ion number. Results obtained from the aforementioned time series are compared and discussed.},
	biburl = {http://www.bibsonomy.org/bibtex/25cbe474e740f7fbe0e885a908133dba4/statphys23},
	keywords = {microsplasmas series time topic-5 electromagnetic confined statphys23 analysis trap}
}