Discrete-Time Langevin Motion in a Gibbs Potential

• 作者: Alexander Roitershtein Jiyeon Suh Reza Rastegar Vadim Roytershteyn
• 来源期刊: 应用数学(英文)
• 学科: 数学
• 关键词: LANGEVIN Equation Dynamics of a Moving Particle MULTIVARIATE REGULAR Variation CHAINS with COMPLETE Connections
• 年，卷（期）: yysxyw_2012,（12）
• 页码范围: 2032-2037
• 页数: 6页
• 分类号: O1

摘要

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.