This paper is concerned with the representation problem of a coupled operator in a product space.A necessary and sufficient condition is given for a class of operators with closed range to have a one-sided coupled ope...This paper is concerned with the representation problem of a coupled operator in a product space.A necessary and sufficient condition is given for a class of operators with closed range to have a one-sided coupled operator matrix representation.The applications of this result in a delay equation and in a diffusion-transport system with dynamical boundary conditions are further presented.展开更多
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 the NNSF of China(Grant Nos.11961052,11761029)the Program for Innovative Research Team in Universities of Inner Mongolia Autonomous Region(Grant No.NMGIRT2317)the NSF of Inner Mongolia(Grant Nos.2021MS01006,2020ZD01)。
文摘This paper is concerned with the representation problem of a coupled operator in a product space.A necessary and sufficient condition is given for a class of operators with closed range to have a one-sided coupled operator matrix representation.The applications of this result in a delay equation and in a diffusion-transport system with dynamical boundary conditions are further presented.
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.
