Successful couplings for a class of stochastic differential equations driven by Lévy processes

被引：0
作者：
HuoNan Lin
Jian Wang
机构：
[1] Fujian Normal University,School of Mathematics and Computer Science
来源：
Science China Mathematics | 2012年 / 55卷
关键词：
stochastic differential equations; Lévy processes; coupling property; coupling operator; Liouville theorem; 60J25; 60J75;
D O I：
暂无
中图分类号：
学科分类号：
摘要：
By constructing proper coupling operators for the integro-differential type Markov generator, we establish the existence of a successful coupling for a class of stochastic differential equations driven by Lévy processes. Our result implies a new Liouville theorem for space-time bounded harmonic functions with respect to the underlying Markov semigroups, and it is sharp for Ornstein-Uhlenbeck processes driven by α-stable Lévy processes.
引用
收藏
页码：1735 / 1748
页数：13
相关论文
共 35 条
  • [11] Cranston M.(1975)Ergodicity and exponential Ann Inst Fourier 25 464-497
  • [12] Wang F. Y.(2004)-mixing bounds for multidimensional diffusions with jumps J Funct Anal 216 455-490
  • [13] Jacob N.(2006)Renaissance, recollements, mélanges, ralentissement de processus de Markov J Funct Anal 236 244-264
  • [14] Schilling R. L.(1986)Liouville theorems for non-local operators Ann Probab 14 271-286
  • [15] Kurenok V.(2011)Gradient estimates for diffusion semigroups with singular coefficeints Ann Inst Henri Poincaré Probab Stat 47 1147-1159
  • [16] Kulik A. M.(2012)On Itô stochastic integration with respect to J Evol Equ 12 119-140
  • [17] Lepeltier J. P.(2011)-stable motion: inner clock, integrability of sample paths, double and multiple integrals Bernoulli 17 1136-1158
  • [18] Marchal B.(2008)On the coupling property of Lévy processes Stoch Proc Appl 118 1909-1928
  • [19] Masuda H.(2010)On the coupling property and the Liouville theorem for Ornstein-Uhlenbeck processes Stoch Proc Appl 120 1680-1700
  • [20] Meyer P. A.(2011)Coupling for Ornstein-Uhlenbeck jump processes Chinese J Contemp Math 32 33-52
1234