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 Levy process...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 Levy 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 s-stable Levy processes.展开更多
基金supported by National Natural Science Foundation of China(Grant No.11126350)the Programme of Excellent Young Talents in Universities of Fujian(Grant Nos.JA10058,JA11051)
文摘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 Levy 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 s-stable Levy processes.
