REGULARITY AND RECURRENCE OF SWITCHING DIFFUSIONS

作     者：George YIN Chao ZHU 

作者机构：Department of Mathematics Wayne State University Detroit Michigan 48202 U.S.A. 

出 版 物：《Journal of Systems Science & Complexity》 (系统科学与复杂性学报（英文版）)

年 卷 期：2007年第20卷第2期

页      面：273-283页

核心收录：

学科分类：02[经济学] 0202[经济学-应用经济学] 020208[经济学-统计学] 07[理学] 0714[理学-统计学（可授理学、经济学学位）] 070103[理学-概率论与数理统计] 0701[理学-数学] 

基　　金：This research is supported in part by the National Science Foundation under DMS-0624849  in part by the National Security Agency under MSPF-068-029  and in part by the National Natural Science Foundation of China under Grant No. 60574069 

主　　题：Recurrence regularity switching diffusion 

摘      要：This work is concerned with switching diffusion processes, also known as regime-switching diffusions. Our attention focuses on regularity, recurrence, and positive recurrence of the underlying stochastic processes. The main effort is devoted to obtaining easily verifiable conditions for the aforementioned properties. Continuous-state-dependent jump processes are considered. First general criteria on regularity and recurrence using Liapunov functions are obtained. Then we focus on a class of problems, in which both the drift and the diffusion coefficients are ＂linearizable＂ with respect to the continuous state, and suppose that the generator of the jump part of the process can be approximated by a generator of an ergodic Markov chain. Sufficient conditions for regularity, recurrence, and positive recurrence are derived, which are linear combination of the averaged coefficients （averaged with respect to the stationary measure of the Markov chain）.