数学物理学报(英文版)

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QUASI-STATIONARY DISTRIBUTIONS FOR THE RADIAL ORNSTEIN-UHLENBECK PROCESSES

叶俊   

  1. 清华大学数学系, 北京 100084
  • 收稿日期:2006-04-20 修回日期:1900-01-01 出版日期:2008-07-20 发布日期:2008-07-20
  • 通讯作者: 叶俊

QUASI-STATIONARY DISTRIBUTIONS FOR THE RADIAL ORNSTEIN-UHLENBECK PROCESSES

Ye Jun   

  1. Department of Mathematical Sciences, Tsinghua University, Beijing 100084, China
  • Received:2006-04-20 Revised:1900-01-01 Online:2008-07-20 Published:2008-07-20
  • Contact: Ye Jun

摘要:

The purpose of this article is to obtain the quasi-stationary distributions of the δ(δ<2)-dimensional radial Ornstein-Uhlenbeck process with
parameter -λ by using the methods of Martinez and San Martin (2001). It is described that the law of this process conditioned on first hitting 0 is just the probability measure induced by a (4-δ)-dimensional radial Ornstein-Uhlenbeck process with parameter -λ. Moreover, it is shown that the law of the conditioned process associated with the left eigenfunction of the process conditioned on first hitting 0 is induced by a one-parameter diffusion.

关键词: Radial Ornstein-Uhlenbeck process, quasi-stationary distribution, quasi-invariant

Abstract:

The purpose of this article is to obtain the quasi-stationary distributions of the δ(δ<2)-dimensional radial Ornstein-Uhlenbeck process with
parameter -λ by using the methods of Martinez and San Martin (2001). It is described that the law of this process conditioned on first hitting 0 is just the probability measure induced by a (4-δ)-dimensional radial Ornstein-Uhlenbeck process with parameter -λ. Moreover, it is shown that the law of the conditioned process associated with the left eigenfunction of the process conditioned on first hitting 0 is induced by a one-parameter diffusion.

Key words: Radial Ornstein-Uhlenbeck process, quasi-stationary distribution, quasi-invariant

中图分类号: 

  • 60F99