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

• Masuda, Hiroki

  Faculty of Mathematics, Kyushu University

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.

Kyushu University 21st Century COE Program Development of Dynamic Mathematics with High Functionality

Journal

• Stochastic Processes and their Applications

  Stochastic Processes and their Applications 117 (1), 35-56, 2007-01

  Elsevier

Keywords

• Diffusion with jumps
• Ergodicity
• Foster–Lyapunov drift criteria
• Irreducibility
• (Exponential) β-mixing property

Details

• CRID: 1050580007682763904
• NII Article ID: 120000981478
• NII Book ID: AA00436340
• HANDLE: 2324/11838
• Text Lang: en
• Article Type: journal article
• Data Source:
  • IRDB
  • CiNii Articles
  • KAKEN