Lévy型过程的耦合及应用

Couplings of Lévy-type processes and applications

本文围绕Lévy型过程的耦合这一主题,综述本文作者在相关问题上开展的阶段性工作.本文分为三部分:(1)Lévy过程的成功耦合;(2)Lévy过程驱动的随机微分方程的耦合构造;(3)耦合方法在Lévy随机系统中的应用.在每部分罗列相关主要研究结果,并着重陈述耦合方法的传承与创新.

In this survey paper,we focus on couplings of Lévy-type processes and expand the paper along with the author's achievements on related topics.The paper consists of three parts:successful couplings for Lévy processes,constructions of couplings for stochastic differential equations driven by Lévy noises,and applications of couplings for stochastic systems with Levy noises.In each part,we list the main related results,and emphatically state the inheritance and innovation of coupling methods.