Jump-diffusions with state-dependent switching: existence and uniqueness, Feller property, linearization, and uniform ergodicity

XI FuBao 已出版文章查询
XI FuBao
xifb@bit.edu.cn, gyin@math.wayne.edu
1 * YIN Gang 已出版文章查询
YIN Gang

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1Department of Mathematics Beijing Institute of Technology Beijing 100081 China

2Department of Mathematics Wayne State University Detroit MI 48202 USA

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.

DOI: http://dx.doi.org/10.1007/s11425-011-4281-y

语种: 英文   

基金Research of the first author was supported in part by Nati...

关键词jump-diffusion sigma-finite characteristic measure state-dependent switching Feller property uniform ergodicity linearization

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