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Discrete-Time Langevin Motion in a Gibbs Potential

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.

Conflicts of Interest

The authors declare no conflicts of interest.

Cite this paper

*Applied Mathematics*, Vol. 3 No. 12A, 2012, pp. 2032-2037. doi: 10.4236/am.2012.312A280.

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