Discrete-time Langevin motion in a Gibbs potential
نویسندگان
چکیده
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.
منابع مشابه
Electron. Commun. Probab. 20 (2015), no. 15, DOI: 10.1214/ECP.v20-3855
In recent papers it has been demonstrated that sampling a Gibbs distribution from an appropriate time-irreversible Langevin process is, from several points of view, advantageous when compared to sampling from a time-reversible one. Adding an appropriate irreversible drift to the overdamped Langevin equation results in a larger large deviations rate function for the empirical measure of the proc...
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تاریخ انتشار 2012