Discrete-Time Langevin Motion in a Gibbs Potential

Reza Rastegar, Alexander Roitershtein, Vadim Roytershteyn, Jiyeon Suh

Department of Electrical and Computer Engineering, University of California San Diego, San Diego, USA.
Department of Mathematics, Grand Valley State University, Allendale, USA.
Department of Mathematics, Iowa State University, Ames, USA.

DOI: 10.4236/am.2012.312A280                

Abstract

We consider a multivariate Langevin equation in discrete time, driven by a force induced by certain Gibbs’states. The main goal of the paper is to study the asymptotic behavior of a random walk with stationary increments (which are interpreted as discrete-time speed terms) satisfying the Langevin equation. We observe that (stable) functional limit theorems and laws of iterated logarithm for regular random walks with i.i.d. heavy-tailed increments can be carried over to the motion of the Langevin particle.

Keywords

Langevin Equation; Dynamics of a Moving Particle; Multivariate Regular Variation; Chains with Complete Connections

Conflicts of Interest

The authors declare no conflicts of interest.

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