TITLE:
Discrete-Time Langevin Motion in a Gibbs Potential
AUTHORS:
Reza Rastegar, Alexander Roitershtein, Vadim Roytershteyn, Jiyeon Suh
KEYWORDS:
Langevin Equation; Dynamics of a Moving Particle; Multivariate Regular Variation; Chains with Complete Connections
JOURNAL NAME:
Applied Mathematics,
Vol.3 No.12A,
December
31,
2012
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.