数学物理学报 ›› 2011, Vol. 31 ›› Issue (3): 785-795.

• 论文 • 上一篇    下一篇

一般对称跳过程的Lyapunov漂移条件

王健   

  1. 福建师范大学数学与计算机科学学院 福建福州 350007
  • 收稿日期:2009-06-11 修回日期:2010-08-04 出版日期:2011-06-25 发布日期:2011-06-25
  • 基金资助:

    福建省自然科学基金(2010J05002)和福建省高校杰出青年科研人才培育计划(JA10058)资助

Lyapunov Drift Conditions for General Symmetric Jump Processes

 WANG Jian   

  1. School of Mathematics and Computer Science, Fujian Normal University, Fuzhou 350007
  • Received:2009-06-11 Revised:2010-08-04 Online:2011-06-25 Published:2011-06-25
  • Supported by:

    福建省自然科学基金(2010J05002)和福建省高校杰出青年科研人才培育计划(JA10058)资助

摘要:

该文旨在考虑一般对称跳过程的Lyapunov漂移条件, 直接通过控制Lyapunov函数来得到关于对称跳过程的Poincaré不等式, 超Poincaré不等式和弱Poincaré不等式成立的充分条件. 同时, 讨论了上述结果在生灭过程和对称Lévy过程中的应用.

关键词: Lyapunov漂移条件, 泛函不等式, 遍历性, 跳过程

Abstract:

This paper studies Lyapunov drift conditions for general symmetric jump processes. The author aims to derive Poincar´e, super-Poincar´e and weak-Poincar´e inequalities directly through Lyapunov functions controls. Birth death processes and symmetric L´evy type processes are presented to illustrate the power of the results.

Key words: Lyapunov drift conditions, Functional inequalities, Ergodic, Jump processes

中图分类号: 

  • 60J25