TY - JOUR
T1 - Ergodicity and exponential β-mixing bounds for multidimensional diffusions with jumps
AU - Masuda, Hiroki
N1 - Funding Information:
This work was partly supported by a Grant-in-Aid for Scientific Research from the Ministry of Education, Japan, Cooperative Research Program of the Institute of Statistical Mathematics, and by the 21st Century COE Program “Development of Dynamic Mathematics with High Functionality” at Kyushu University.
PY - 2007/1
Y1 - 2007/1
N2 - 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.
AB - 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.
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U2 - 10.1016/j.spa.2006.04.010
DO - 10.1016/j.spa.2006.04.010
M3 - Article
AN - SCOPUS:33751319255
SN - 0304-4149
VL - 117
SP - 35
EP - 56
JO - Stochastic Processes and their Applications
JF - Stochastic Processes and their Applications
IS - 1
ER -