Ergodicity and exponential β-mixing bounds for multidimensional diffusions with jumps

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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 β-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.

Original languageEnglish
Pages (from-to)35-56
Number of pages22
JournalStochastic Processes and their Applications
Volume117
Issue number1
DOIs
Publication statusPublished - Jan 2007

All Science Journal Classification (ASJC) codes

  • Statistics and Probability
  • Modelling and Simulation
  • Applied Mathematics

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