Generalized Langevin equation driven by Lévy processes: A probabilistic, numerical and time series based approach

Autor:	Chang C. Y. Dorea, Rafael Morgado, Ary V. Medino, Sílvia R. C. Lopes
Rok vydání:	2012
Předmět:	Statistics and Probability Langevin equation Stochastic differential equation Mathematical optimization Series (mathematics) Convergence of random variables Anomalous diffusion Stochastic process Monte Carlo method Applied mathematics Condensed Matter Physics Lévy process Mathematics
Zdroj:	Physica A: Statistical Mechanics and its Applications. 391:572-581
ISSN:	0378-4371
DOI:	10.1016/j.physa.2011.09.025
Popis:	Levy processes have been widely used to model a large variety of stochastic processes under anomalous diffusion. In this note we show that Levy processes play an important role in the study of the Generalized Langevin Equation (GLE). The solution to the GLE is proposed using stochastic integration in the sense of convergence in probability. Properties of the solution processes are obtained and numerical methods for stochastic integration are developed and applied to examples. Time series methods are applied to obtain estimation formulas for parameters related to the solution process. A Monte Carlo simulation study shows the estimation of the memory function parameter. We also estimate the stability index parameter when the noise is a Levy process.
Databáze:	OpenAIRE
Externí odkaz:	https://explore.openaire.eu/search/publication?articleId=doi_________::0ad10351d0eec8d96875dc564026b1a8 https://doi.org/10.1016/j.physa.2011.09.025 Zobrazit plný text záznamu Full Text from ScienceDirect