A. Novikov and N. Kordzakhia, “Martingales and First Passage Times of AR(1) Sequences,” Stochastics, Vol. 80, No. 2-3, 2008, pp. 197-210. doi:10.1080/17442500701840885

has been cited by the following article:

• 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.