数学物理学报(英文版) ›› 2015, Vol. 35 ›› Issue (6): 1426-1436.doi: 10.1016/S0252-9602(15)30064-3

• 论文 • 上一篇    下一篇

MOMENTS OF PASSAGE TIMES AND ASYMPTOTIC BEHAVIOR OF INCREASING SELF-SIMILAR MARKOV PROCESSES

胡巍1,2, 刘禄勤2   

  1. 1. Department of Mathematics, Jiangsu University of Technology, Changzhou 213001, China;
    2. School of Mathematics and Statistics, Wuhan University, Wuhan 430072, China
  • 收稿日期:2015-04-26 修回日期:2014-07-10 出版日期:2015-11-01 发布日期:2015-11-01
  • 作者简介:Wei HU, E-mail: huw721@whu.edu.cn;Luqin LIU, E-mail: lqliu@whu.edu.cn
  • 基金资助:

    Research supported in part by the National Natural Science Foundation of China (11171262, 11171263).

MOMENTS OF PASSAGE TIMES AND ASYMPTOTIC BEHAVIOR OF INCREASING SELF-SIMILAR MARKOV PROCESSES

Wei HU1,2, Luqin LIU2   

  1. 1. Department of Mathematics, Jiangsu University of Technology, Changzhou 213001, China;
    2. School of Mathematics and Statistics, Wuhan University, Wuhan 430072, China
  • Received:2015-04-26 Revised:2014-07-10 Online:2015-11-01 Published:2015-11-01
  • Supported by:

    Research supported in part by the National Natural Science Foundation of China (11171262, 11171263).

摘要:

By using Lamperti's bijection between self-similar Markov processes and Lévy processes, we prove finiteness of moments and asymptotic behavior of passage times for increasing self-similar Markov processes valued in (0,∞). We also investigate the behavior of the process when it crosses a level. A limit theorem concerning the distribution of the process immediately before it crosses some level is proved. Some useful examples are given.

关键词: self-similar process, Markov process, Lé, vy process, subordinator, passage time, moment

Abstract:

By using Lamperti's bijection between self-similar Markov processes and Lévy processes, we prove finiteness of moments and asymptotic behavior of passage times for increasing self-similar Markov processes valued in (0,∞). We also investigate the behavior of the process when it crosses a level. A limit theorem concerning the distribution of the process immediately before it crosses some level is proved. Some useful examples are given.

Key words: self-similar process, Markov process, Lé, vy process, subordinator, passage time, moment

中图分类号: 

  • 60G18