This work focuses on a class of jump-diffusions with state-dependent switching. First, compared with the existing results in the literature, in our model, the characteristic measure is allowed to be σ-finite. The exi...This work focuses on a class of jump-diffusions with state-dependent switching. First, compared with the existing results in the literature, in our model, the characteristic measure is allowed to be σ-finite. The existence and uniqueness of the underlying process are obtained by representing the switching component as a stochastic integral with respect to a Poisson random measure and by using a successive approximation method. Then, the Feller property is proved by means of introducing auxiliary processes and by making use of Radon-Nikodym derivatives. Furthermore, the irreducibility and all compact sets being petite are demonstrated. Based on these results, the uniform ergodicity is established under a general Lyapunov condition. Finally, easily verifiable conditions for uniform ergodicity are established when the jump-diffusions are linearizable with respect to the variable x (the state variable corresponding to the jump-diffusion component) in a neighborhood of the infinity, and some examples are presented to illustrate the results.展开更多
This work is concerned with successful couplings for a class of multidimensional difusion processes with state-dependent switching.We construct a type of couplings for this class of processes,and give some sufcient co...This work is concerned with successful couplings for a class of multidimensional difusion processes with state-dependent switching.We construct a type of couplings for this class of processes,and give some sufcient conditions to guarantee this type of couplings to be successful.Besides,two illustrative examples are provided.展开更多
基金supported in part by National Natural Science Foundation of China(Grant No. 11171024)supported in part by National Natural Science Foundation of China (Grant No.70871055)supported in part by National Science Foundationof US (Grant No. DMS-0907753)
文摘This work focuses on a class of jump-diffusions with state-dependent switching. First, compared with the existing results in the literature, in our model, the characteristic measure is allowed to be σ-finite. The existence and uniqueness of the underlying process are obtained by representing the switching component as a stochastic integral with respect to a Poisson random measure and by using a successive approximation method. Then, the Feller property is proved by means of introducing auxiliary processes and by making use of Radon-Nikodym derivatives. Furthermore, the irreducibility and all compact sets being petite are demonstrated. Based on these results, the uniform ergodicity is established under a general Lyapunov condition. Finally, easily verifiable conditions for uniform ergodicity are established when the jump-diffusions are linearizable with respect to the variable x (the state variable corresponding to the jump-diffusion component) in a neighborhood of the infinity, and some examples are presented to illustrate the results.
基金supported by National Natural Science Foundation of China(Grant No.11171024)Foundation for the Author of National Excellent Doctoral Dissertation of China(Grant No.200917)
文摘This work is concerned with successful couplings for a class of multidimensional difusion processes with state-dependent switching.We construct a type of couplings for this class of processes,and give some sufcient conditions to guarantee this type of couplings to be successful.Besides,two illustrative examples are provided.
