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

Ary V. Medino, Sílvia R.C. Lopes, Rafael Morgado and Chang C.Y. Dorea

Physica A: Statistical Mechanics and its Applications, 2012, vol. 391, issue 3, 572-581

Abstract: Lévy processes have been widely used to model a large variety of stochastic processes under anomalous diffusion. In this note we show that Lévy 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 Lévy process.

Keywords: Lévy processes; Langevin equation; Anomalous diffusion; Time series (search for similar items in EconPapers)
Date: 2012
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Citations: View citations in EconPapers (4)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:391:y:2012:i:3:p:572-581

DOI: 10.1016/j.physa.2011.09.025

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