Ergodicity and exponential [beta]-mixing bounds for multidimensional diffusions with jumps

Hiroki Masuda

Stochastic Processes and their Applications, 2007, vol. 117, issue 1, 35-56

Abstract: Let X be a multidimensional diffusion with jumps. We provide sets of conditions under which: X fulfils the ergodic theorem for any initial distribution; and X is exponentially [beta]-mixing. Utilizing the Foster-Lyapunov drift criteria developed by Meyn and Tweedie, we extend several existing results concerning diffusions. We also obtain the boundedness of moments of g(Xt) for a suitable unbounded function g. Our results can cover a wide variety of diffusions with jumps by selecting suitable test functions, and serve as fundamental tools for statistical analyses concerning the processes.

Keywords: Diffusion; with; jumps; Ergodicity; Foster-Lyapunov; drift; criteria; Irreducibility; (Exponential); [beta]-mixing; property (search for similar items in EconPapers)
Date: 2007
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Citations: View citations in EconPapers (14)

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