%0 Book Section %1 statphys23_0052 %A Gleria, I.M. %A Figueiredo, A.D. %A Dasilva, S. %A Matsushita, R. %B Abstract Book of the XXIII IUPAP International Conference on Statistical Physics %C Genova, Italy %D 2007 %E Pietronero, Luciano %E Loreto, Vittorio %E Zapperi, Stefano %K convergence correlations econophysics exchange foreign laws nonlinear power rates slow statphys23 topic-11 %T Nonlinear correlations, power laws and slow convergence to the gaussian %U http://st23.statphys23.org/webservices/abstract/preview_pop.php?ID_PAPER=52 %X In recent papers we have shown that the sluggish convergence of truncated L\' evy flights 1 to the Gaussian distribution and the presence of scaling power laws in their probability of return to the origin can be explained by autocorrelation in data 2,3. Here we enlarge the scope of our results considering the role of generalized nonlinear correlations. The role of the correlations in the convergence process as well as the problem of establishing the distance of a given distribution to the Gaussian are analyzed in detail. We show that whereas power laws in the second moment can still be explained by linear correlation of pairs, slow convergence emerge from nonlinear correlations. Our approach is exemplified with data from foreign exchange rate 4,5.\\ 1) R.N. Mantegna, H.E. Stanley, Stochastic process with ultraslow convergence to a Gaussian: the truncated Levy flight, Phys. Rev. Lett. 73 (1994) 2946-2949.\\ 2) A. Figueiredo, I. Gleria, R. Matsushita, S. Da Silva, Autocorrelation as a source of truncated Levy flights in foreign exchange rates, Physica A 323 (2003), 601-625.\\ 3) A. Figueiredo, I. Gleria, R. Matsushita, S. Da Silva, On the origins of truncated Levy flights, Phys. Lett. A 315 (2003) 51-60.\\ 4) I. Gleria, A. Figueiredo, R. Matsushita, S. Da Silva, Levy flights, autocorrelation ans slow convergente, Physica A 337 (2004), 369-383.\\ 5) S. Da Silva,R. Matsushita, I. Gleria, A. Figueiredo, P. Rathie, International finance, Levy distributions, and the econophysics of exchange rates, Communications in Nonlinear Science and Numerical Simulations 10 (2005), 365-393.

@incollection{statphys23_0052, abstract = {In recent papers we have shown that the sluggish convergence of truncated L\' evy flights [1] to the Gaussian distribution and the presence of scaling power laws in their probability of return to the origin can be explained by autocorrelation in data [2,3]. Here we enlarge the scope of our results considering the role of generalized nonlinear correlations. The role of the correlations in the convergence process as well as the problem of establishing the distance of a given distribution to the Gaussian are analyzed in detail. We show that whereas power laws in the second moment can still be explained by linear correlation of pairs, slow convergence emerge from nonlinear correlations. Our approach is exemplified with data from foreign exchange rate [4,5].\\ 1) R.N. Mantegna, H.E. Stanley, {\it Stochastic process with ultraslow convergence to a Gaussian: the truncated Levy flight}, Phys. Rev. Lett. {\bf 73} (1994) 2946-2949.\\ 2) A. Figueiredo, I. Gleria, R. Matsushita, S. Da Silva, {\it Autocorrelation as a source of truncated Levy flights in foreign exchange rates}, Physica A {\bf 323} (2003), 601-625.\\ 3) A. Figueiredo, I. Gleria, R. Matsushita, S. Da Silva, {\it On the origins of truncated Levy flights}, Phys. Lett. A {\bf 315} (2003) 51-60.\\ 4) I. Gleria, A. Figueiredo, R. Matsushita, S. Da Silva, {\it Levy flights, autocorrelation ans slow convergente}, Physica A {\bf 337} (2004), 369-383.\\ 5) S. Da Silva,R. Matsushita, I. Gleria, A. Figueiredo, P. Rathie, {\it International finance, Levy distributions, and the econophysics of exchange rates}, Communications in Nonlinear Science and Numerical Simulations {\bf 10} (2005), 365-393.}, added-at = {2007-06-20T10:16:09.000+0200}, address = {Genova, Italy}, author = {Gleria, I.M. and Figueiredo, A.D. and Dasilva, S. and Matsushita, R.}, biburl = {https://www.bibsonomy.org/bibtex/2b5d6db8bd0149d8eaa45431b6b93881c/statphys23}, booktitle = {Abstract Book of the XXIII IUPAP International Conference on Statistical Physics}, editor = {Pietronero, Luciano and Loreto, Vittorio and Zapperi, Stefano}, interhash = {e1b1c2d5655ef1bd7419b8f078f414f0}, intrahash = {b5d6db8bd0149d8eaa45431b6b93881c}, keywords = {convergence correlations econophysics exchange foreign laws nonlinear power rates slow statphys23 topic-11}, month = {9-13 July}, timestamp = {2007-06-20T10:16:10.000+0200}, title = {Nonlinear correlations, power laws and slow convergence to the gaussian}, url = {http://st23.statphys23.org/webservices/abstract/preview_pop.php?ID_PAPER=52}, year = 2007 }