数学物理学报 ›› 2009, Vol. 29 ›› Issue (4): 1051-1057.

• 论文 • 上一篇    下一篇

带马氏切换的马氏过程的指数收敛速度

  

  1. (北京理工大学 数学系, 北京 100081)
  • 收稿日期:2007-03-11 修回日期:2008-09-24 出版日期:2009-08-25 发布日期:2009-08-25
  • 基金资助:

    国家自然科学基金(10671037)资助

Exponential Convergence Rates for Markov Processes with Markovian Switching

  1. (Department of Mathematics, Beijing Institute of Technology, Beijing 100081)
  • Received:2007-03-11 Revised:2008-09-24 Online:2009-08-25 Published:2009-08-25
  • Supported by:

    国家自然科学基金(10671037)资助

摘要:

设 (X(t), Z(t)) 是以[0, ∞) ×{1, 2, …, n0} 为状态空间的强马氏过程, 其第一分量 X(t) 依赖于第二分量 Z(t), 而第二分量 Z(t) 是一个马氏链. 应用耦合方法, 估计了(X(t), Z(t)) 的转移概率依全变差范数收敛于其不变概率测度的指数收敛速度.

关键词: 马氏切换, 耦合, 指数收敛速度, 全变差

Abstract:

Let (X(t), Z(t)) be a strong Markov process with the phase space [0, ∞) ×{1, 2, …, n0} such that the first component X(t) depends on the second component Z(t) which is a Markov chain. Using the coupling methods, the author evaluates the exponential convergence rates of the transition probability of (X(t), Z(t)) to its invariant probability measure in total variation norm.

Key words: Markovian switching, Coupling, Exponential convergence rate, Total variation

中图分类号: 

  • 60K25