Strong ergodicity of the regime-switching diffusion processes |
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Authors: | Jinghai Shao Fubao Xi |
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Institution: | 1. School of Mathematical Sciences, Beijing Normal University, Beijing, China;2. School of Mathematics, Beijing Institute of Technology, Beijing 100081, China |
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Abstract: | We provide criteria for the strong ergodicity of regime-switching diffusion processes. Our conditions are imposed on the coefficients of the processes. Particularly, we show that for regime-switching diffusions on the half line, if the corresponding diffusion on each fixed environment is strongly ergodic, then the regime-switching diffusion is strongly ergodic as well, which does not depend on the changing rate of the environment. Moreover, the converse is not always true, which is shown by an example. For transience, recurrence and positive recurrence, there is no such good consistency R. Pinsky and M. Scheutzow, Some remarks and examples concerning the transience and recurrence of random diffusions, Ann. Inst. Henri. Poincaré 28 (1992) 519–536]. |
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Keywords: | Regime-switching diffusions Strong ergodicity Successful couplings Lyapunov functions |
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