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| 1 | On the stability of diffusion processes with state-dependent switching显示文摘In this paper we consider the stability for diffusion processes with state-dependent switching. We first prove their Feller continuity by the coupling methods. Furthermore, we also prove their strong Feller continuity and their exponential ergodicity under some reasonable conditions. Finally, we append a very brief discussion about the regularity of these processes. | XI Fubao & ZHAO Liqin Department of Mathematics, Beijing Institute of Technology, Beijing 100081, China School of Mathematical Sciences, Beijing Normal University, Beijing 100875, China | 2006 | Science China Mathematics2006，49，9： | 5 |
| 2 | Jump-diffusions with state-dependent switching:existence and uniqueness,Feller property,linearization,and uniform ergodicity显示文摘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. | XI FuBao YIN Gang | 2011 | Science China Mathematics2011，54，12： | 3 |
| 3 | Successful couplings for difusion processes with state-dependent switching显示文摘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. | XI FuBao SHAO JingHai | 2013 | Science China Mathematics2013，56，10： | 2 |
| 4 | Feller property and exponential ergodicity of diffusion processes with state-dependent switching显示文摘In this paper we consider the Feller property and the exponential ergodicity for general diffusion processes with state-dependent switching. We prove their Feller continuity by means of intro- ducing some auxiliary processes and by making use of the Radon-Nikodym derivatives. Furthermore, we also prove their strong Feller continuity and their exponential ergodicity under some reasonable conditions. | XI FuBao Department of Mathematics, Beijing Institute of Technology, Beijing 100081, China | 2008 | Science China Mathematics2008，51，3： | 2 |
| 5 | Large deviations for empirical measures of switching diffusion processes with small parameters显示文摘我们与 Markovian 切换考虑散开过程的 asymptotic 性质。为一个一般盒子,我们为与小参数交换散开过程的实验措施证明一个大偏差原则。 | Xiaocui MA Fubao XI | 2015 | Frontiers of Mathematics in China2015，10，4： | 1 |
| 6 | Stability for a random evolution equation with Gaussian perturbation显示文摘 | Fubao Xi | 2002 | J Math AnaIAppl2002，272，： | 1 |
| 7 | Stability for a random evolution equation with Gaussian perturbation显示文摘 | Xi Fubao | 2002 | J Math Anal Appl2002，，272： | 1 |
| 8 | Small Random Perturbations of One-Dimensional Diffusion Processes | Xi Fubao Department of Applied Mathematics, Beijing Institute of Technology, Beijing 100081, China | 1998 | Acta Mathematica Sinica,English Series1998，14，1： | 0 |
| 9 | Moderate deviations for neutral functional stochastic differential equations driven by Levy noises显示文摘Using the weak convergence method introduced by A.Budhiraja,P.Dupuis,and A.Ganguly[Ann.Probab.,2016,44:1723-1775],we establish the moderate deviation principle for neutral functional stochastic differential equations driven by both Brownian motions and Poisson random measures. | Xiaocui MA Fubao XI Dezhi LIU | 2020 | Frontiers of Mathematics in China2020，15，3： | 0 |
| 10 | Convergence,boundedness,and ergodicity of regime-switching diusion processes with infinite memory显示文摘We study a class of diffusion processes, which are determined by solutions X(t) to stochastic functional differential equation with infinite memory and random switching represented by Markov chain Λ(t): Under suitable conditions, we investigate convergence and boundedness of both the solutions X(t) and the functional solutions Xt: We show that two solutions (resp., functional solutions) from different initial data living in the same initial switching regime will be close with high probability as time variable tends to infinity, and that the solutions (resp., functional solutions) are uniformly bounded in the mean square sense. Moreover, we prove existence and uniqueness of the invariant probability measure of two-component Markov-Feller process (Xt,Λ(t));and establish exponential bounds on the rate of convergence to the invariant probability measure under Wasserstein distance. Finally, we provide a concrete example to illustrate our main results. | Jun LI Fubao XI | 2021 | Frontiers of Mathematics in China2021，16，2： | 0 |
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