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R. Fernández and G. Maillard, “Chains with Complete Connections: General Theory, Uniqueness, Loss of Memory and Mixing Properties,” Journal of Statistical Physics, Vol. 118, No. 3-4, 2005, pp. 555-588. doi:10.1007/s10955-004-8821-5

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.