BibSonomyburst/tag/excursionsBibSonomy RSS feed for /tag/excursions2012-02-15T20:25:00+01:00http://www.bibsonomy.org/bibtex/232487a00421279724f13507d75b3e2d1/peter.ralphpeter.ralph2010-08-26T21:00:05+02:00diffusions excursions hitting_times laplace_transform <span class="authorEditorList"><a href="/author/Pitman">Jim Pitman</a>, and <a href="/author/Yor">Marc Yor</a> </span><em>Bernoulli</em> <em>5(2):pp. 249-255</em> (<em>1999</em>)Thu Aug 26 21:00:05 CEST 2010Bernoulli2pp. 249-255Laplace Transforms Related to Excursions of a One-Dimensional Diffusion51999diffusions excursions hitting_times laplace_transform Various known expressions in terms of hyperbolic functions for the Laplace transforms of random times related to one-dimensional Brownian motion are derived in a unified way by excursion theory and extended to one-dimensional diffusions.http://www.bibsonomy.org/bibtex/2af18ef33b84971e852358ff3c9728f8d/peter.ralphpeter.ralph2010-08-26T20:57:36+02:00diffusions excursions hitting_times laplace_transform local_times occupation_time review <span class="authorEditorList"><a href="/author/Pitman">Jim Pitman</a>, and <a href="/author/Yor">Marc Yor</a> </span><em>Bernoulli</em> <em>9(1):1-24</em> (<em>2003</em>)Thu Aug 26 20:57:36 CEST 2010Bernoulli 11-24Hitting, occupation and inverse local times of one-dimensional diffusions: {Martingale} and excursion approaches.92003diffusions excursions hitting_times laplace_transform local_times occupation_time review {Summary: Basic relations between the distributions of hitting, occupation and inverse local times of a one-dimensional diffusion process $X$, first discussed by {\it K. It\^o} and {\it H. P. McKean jun.} [``Diffusion processes and their sample paths'' (1965; Zbl 0127.09503)], are reviewed from the perspectives of martingale calculus and excursion theory. These relations, and the technique of conditioning on $L^y_T$, the local time of $X$ at level $y$ before a suitable random time $T$, yield formulae for the joint Laplace transform of $L^y_T$ and the times spent by $X$ above and below level $y$ up to time $T$.}http://www.bibsonomy.org/bibtex/2c36b8cb697027e4d7261bae24c95a168/peter.ralphpeter.ralph2010-01-15T19:31:30+01:00Poisson_process excursions size_biased_parititions <span class="authorEditorList"><a href="/author/Perman">M. Perman</a>, <a href="/author/Pitman">J. Pitman</a>, and <a href="/author/Yor">M. Yor</a> </span><em>Probability Theory and Related Fields</em> <em>92(1):21--39</em> (<em>1992</em>)Fri Jan 15 19:31:30 CET 2010Probability Theory and Related Fields121--39{Size-biased sampling of Poisson point processes and excursions}921992Poisson_process excursions size_biased_parititions ome general formulae are obtained for size-biased sampling from a Poisson point process in an abstract space where the size of a point is defined by an arbitrary strictly positive function. These formulae explain why in certain cases (gamma and stable) the size-biased permutation of the normalized jumps of a subordinator can be represented by a stickbreaking (residual allocation) scheme defined by independent beta random variables. An application is made to length biased sampling of excursions of a Markov process away from a recurrent point of its statespace, with emphasis on the Brownian and Bessel cases when the associated inverse local time is a stable subordinator. Results in this case are linked to generalizations of the arcsine law for the fraction of time spent positive by Brownian motion.http://www.bibsonomy.org/bibtex/2868b2332af933348e30042a963ace490/peter.ralphpeter.ralph2009-04-25T01:55:19+02:00Poisson_Dirichlet_distribution exchangeability excursions partitions reference sampling_formula <span class="authorEditorList"><a href="/author/Pitman">J. Pitman</a> </span><em>Lecture Notes-Monograph Series</em> (<em>2003</em>)Sat Apr 25 01:55:19 CEST 2009Lecture Notes-Monograph Series1--34{Poisson-Kingman partitions}2003Poisson_Dirichlet_distribution exchangeability excursions partitions reference sampling_formula This paper presents some general formulas for random partitions of a finite set derived by Kingman's model of random sampling from an interval partition generated by subintervals whose lengths are the points of a Poisson point process. These lengths can be also interpreted as the jumps of a subordinator, that is an increasing process with stationary independent increments. Examples include the two-parameter family of Poisson-Dirichlet models derived from the Poisson process of jumps of a stable sub- ordinator. Applications are made to the random partition generated by the lengths of excursions of a Brownian motion or Brownian bridge conditioned on its local time at zero. {Poisson-Kingman partitions}http://www.bibsonomy.org/bibtex/207931e3aac0bf06022d5984877d60b04/peter.ralphpeter.ralph2009-04-24T23:33:01+02:00excursions quasidiffusions spectral_theory <span class="authorEditorList"><a href="/author/Küchler">Uwe Küchler</a> </span><em>Publ. Res. Inst. Math. Sci.</em> <em>16(1):245--268</em> (<em>1980</em>)Fri Apr 24 23:33:01 CEST 2009Publ. Res. Inst. Math. Sci.1245--268Some asymptotic properties of the transition densities of one-dimensional quasidiffusions161980excursions quasidiffusions spectral_theory q-paperhttp://www.bibsonomy.org/bibtex/28c52b2b13279e8d54c02b0fb4c02f9a9/peter.ralphpeter.ralph2009-04-24T23:33:01+02:00excursions quasidiffusions spectral_theory <span class="authorEditorList"><a href="/author/Küchler">Uwe Küchler</a> </span><em>Math. Operationsforsch. Statist. Ser. Statist.</em> <em>13(2):219--230</em> (<em>1982</em>)Fri Apr 24 23:33:01 CEST 2009Math. Operationsforsch. Statist. Ser. Statist.2219--230Exponential families of {M}arkov processes. {II}. {B}irth-and-death processes131982excursions quasidiffusions spectral_theory q-paperhttp://www.bibsonomy.org/bibtex/2415dbbd8efc0c62092b8f79a8f2693b6/peter.ralphpeter.ralph2009-04-24T23:33:01+02:00excursions quasidiffusions spectral_theory <span class="authorEditorList"><a href="/author/Küchler">Uwe Küchler</a> </span><em>Math. Operationsforsch. Statist. Ser. Statist.</em> <em>13(1):57--69</em> (<em>1982</em>)Fri Apr 24 23:33:01 CEST 2009Math. Operationsforsch. Statist. Ser. Statist.157--69Exponential families of {M}arkov processes. {I}. {G}eneral results131982excursions quasidiffusions spectral_theory q-paperhttp://www.bibsonomy.org/bibtex/27eafb45253187674f7b43acd62344cb1/peter.ralphpeter.ralph2009-04-24T23:33:01+02:00excursions quasidiffusions spectral_theory <span class="authorEditorList"><a href="/author/Küchler">Uwe Küchler</a> </span><em>Probability theory and mathematical statistics, Vol.\ II Vilnius, 1985, </em><em>VNU Sci. Press, </em><em>Utrecht, </em>(<em>1987</em>)Fri Apr 24 23:33:01 CEST 2009UtrechtProbability theory and mathematical statistics, Vol.\ II (Vilnius, 1985)161--165On {I}t\^o's excursion law, local times and spectral measures for quasidiffusions1987excursions quasidiffusions spectral_theory condensed version of "On sojourn times..." q-paperhttp://www.bibsonomy.org/bibtex/2534e34f8c9a769b48b2218948eed041d/peter.ralphpeter.ralph2009-04-24T23:33:01+02:00excursions quasidiffusions spectral_theory <span class="authorEditorList"><a href="/author/Küchler">Uwe Küchler</a> </span><em>Markov processes and control theory Gauß ig, 1988, </em><em>volume 54 of Math. Res., </em><em>Akademie-Verlag, </em><em>Berlin, </em>(<em>1989</em>)Fri Apr 24 23:33:01 CEST 2009BerlinMarkov processes and control theory (Gau\ss ig, 1988)100--103Math. Res.A limit theorem for the excursion of quasidiffusions straddling {$t$}541989excursions quasidiffusions spectral_theory q-paperhttp://www.bibsonomy.org/bibtex/2a63480d9c07006befd87872623bbc116/peter.ralphpeter.ralph2009-04-24T23:33:01+02:00excursions spectral_theory <span class="authorEditorList"><a href="/author/Küchler">Uwe Küchler</a> </span><em>C. R. Acad. Bulgare Sci.</em> <em>38(11):1445--1448</em> (<em>1985</em>)Fri Apr 24 23:33:01 CEST 2009C. R. Acad. Bulgare Sci.111445--1448Quasidiffusions, sojourn times and spectral measures381985excursions spectral_theory q-paperhttp://www.bibsonomy.org/bibtex/283f87ce5fb90f6885ae7b0ccfab06446/peter.ralphpeter.ralph2009-04-24T23:33:01+02:00excursions quasidiffusions spectral_theory <span class="authorEditorList"><a href="/author/Küchler">Uwe Küchler</a> </span><em>J. Math. Kyoto Univ.</em> <em>26(3):403--421</em> (<em>1986</em>)Fri Apr 24 23:33:01 CEST 2009J. Math. Kyoto Univ.3403--421On sojourn times, excursions and spectral measures connected with quasidiffusions261986excursions quasidiffusions spectral_theory q-paperhttp://www.bibsonomy.org/bibtex/2a46c28a46dc7cd2c51757d95eb542856/peter.ralphpeter.ralph2009-04-01T01:40:08+02:00GEM_distribution Poisson_Dirichlet_distribution coalescent_theory excursions partitions subordinators urn_models <span class="authorEditorList"><a href="/author/Pitman">J. Pitman</a>, and <a href="/author/Yor">M. Yor</a> </span><em>Annals of Probability</em> <em>25(2):855--900</em> (<em>1997</em>)Wed Apr 01 01:40:08 CEST 2009Annals of Probability2855--900{The two-parameter Poisson-Dirichlet distribution derived from a stable subordinator}251997GEM_distribution Poisson_Dirichlet_distribution coalescent_theory excursions partitions subordinators urn_models The two-parameter Poisson-Dirichlet distribution, denoted $\mathsf{PD}(\alpha, \theta)$ is a probability distribution on the set of decreasing positive sequences with sum 1. The usual Poisson-Dirichlet distribution with a single parameter $\theta$, introduced by Kingman, is $\mathsf{PD}(0, \theta)$. Known properties of $\mathsf{PD}(0, \theta)$, including the Markov chain description due to Vershik, Shmidt and Ignatov, are generalized to the two-parameter case. The size-biased random permutation of $\mathsf{PD}(\alpha, \theta)$ is a simple residual allocation model proposed by Engen in the context of species diversity, and rediscovered by Perman and the authors in the study of excursions of Brownian motion and Bessel processes. For $0 < \alpha < 1, \mathsf{PD}(\alpha, 0)$ is the asymptotic distribution of ranked lengths of excursions of a Markov chain away from a state whose recurrence time distribution is in the domain of attraction of a stable law of index $\alpha$. Formulae in this case trace back to work of Darling, Lamperti and Wendel in the 1950s and 1960s. The distribution of ranked lengths of excursions of a one-dimensional Brownian motion is $\mathsf{PD}(1/2, 0)$, and the corresponding distribution for a Brownian bredge is $\mathsf{PD}(1/2, 1/2)$. The $\mathsf{PD}(\alpha, 0)$ and $\mathsf{PD}(\alpha, \alpha)$ distributions admit a similar interpretation in terms of the ranked lengths of excursions of a semistable Markov process whose zero set is the range of a stable subordinator of index $\alpha$.http://www.bibsonomy.org/bibtex/29d9bd81822f18fb8d04375eea4c9b8c7/smichasmicha2008-04-22T14:25:45+02:00Excursions <span class="authorEditorList"><a href="/author/Scheffer">Carel L. Scheffer</a> </span><em>Stochastic Processes and their Applications</em> <em>55(1):101--118</em> (<em>January 1995</em>)Tue Apr 22 14:25:45 CEST 2008Stochastic Processes and their ApplicationsJan1101--118The rank of the present excursion551995Excursions Stochastic Processes and their Applicationshttp://www.bibsonomy.org/bibtex/29f4390d7d0965c4c7371b02ddd8f6c7b/statphys23statphys232007-06-20T10:16:09+02:00anomalous bernoulli diffusion excursions fractional linear motion stable statphys23 topic-3 <span class="authorEditorList"><a href="/author/Watkins">N.W. Watkins</a>, <a href="/author/Credgington">D. Credgington</a>, <a href="/author/Sanchez">R. Sanchez</a>, and <a href="/author/Chapman">S.C. Chapman</a> </span><em>Abstract Book of the XXIII IUPAP International Conference on Statistical Physics, </em><em>Genova, Italy, </em>(<em>September 2007</em>)Wed Jun 20 10:16:09 CEST 2007Genova, ItalyAbstract Book of the XXIII IUPAP International Conference on Statistical Physics9-13 JulyA diffusion equation for linear fractional stable motion, apparent multifractality \& applications to space physics2007anomalous bernoulli diffusion excursions fractional linear motion stable statphys23 topic-3 In the 1960s Mandelbrot developed the use of fractals to describe how the shape of many aspects of the natural world departs from the Euclidean. In particular he proposed two kinds of fractal model to capture the way in which natural data is often persistent in time (his Joseph effect, common in hydrology and exemplified by fractional Brownian motion) and or prone to heavy tailed jumps (the Noah effect, typical of economic index time series, for which he gave L\'{e}vy flights as an exemplar). Both effects are now well demonstrated in proxies both for the Earth's auroral electric currents and for the turbulent solar wind which is their ultimate energy source. Modelling, however, has usually emphasised one of the Noah and Joseph parameters (the tail exponent $\mu$ and one derived from the temporal behaviour such as power spectral $\beta$) at the other's expense. This poster will first describe recent work [1] in which we applied a simple self-affine stable model-linear fractional stable motion, LFSM, which unifies both effects-to give insight into space physics data. I will show how we have resolved some contradictions seen in earlier work, where purely Joseph or Noah descriptions had been sought. Such hybrid Noah-Joseph ambivalent [2] behaviour is highly topical in physics. It is typically studied in the paradigm of the continuous time random walk (CTRW) rather than LFSM. Intriguingly the self-similarity exponent extracted from the CTRW differs from that seen in LFSM, being a ratio of $\mu$ and a temporal exponent rather than an additive function. The poster will elucidate the physical differences between these two pictures with reference to a newly-derived diffusion equation for LFSM, which replaces the second order spatial derivative in the equation of fBm [3] with a fractional derivative of order $\mu$. I will also show work in progress using an LFSM generator and simple analytic scaling arguments to study the problem of the area between a fractional L\'{e}vy curve and a threshold-related both to Bernoulli excursions and to the burst size measure introduced by Takalo and Consolini into solar-terrestrial physics and further studied by Freeman et al [4,5]. Finally I will discuss how LFSM gives the appearance of multi-affine scaling without having an underlying turbulent cascade or other multiplicative process. The importance of this property for the interpretation of natural time series will be discussed. 1) Watkins et al, Space Sci. Rev. 121, 271, 2005.\\ 2) Brockmann et al, Nature 439, 462, 2006.\\ 3) Wang and Lung, Phys. Lett. A 151, 119, 1990.\\ 4) Freeman et al, Geophys. Res. Lett. 27, 1367, 2000.\\ 5) Freeman et al, Phys. Rev. E 62, 8794, 2000.