AM  Vol.3 No.12 A , December 2012
Discrete-Time Langevin Motion in a Gibbs Potential
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.


Cite this paper
R. Rastegar, A. Roitershtein, V. Roytershteyn and J. Suh, "Discrete-Time Langevin Motion in a Gibbs Potential," Applied Mathematics, Vol. 3 No. 12, 2012, pp. 2032-2037. doi: 10.4236/am.2012.312A280.
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