Articles

QUASI-STATIONARY DISTRIBUTIONS FOR THE RADIAL ORNSTEIN-UHLENBECK PROCESSES

  • Ye Jun
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  • Department of Mathematical Sciences, Tsinghua University, Beijing 100084, China

Received date: 2006-04-20

  Revised date: 1900-01-01

  Online published: 2008-07-20

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.

Cite this article

Ye Jun . QUASI-STATIONARY DISTRIBUTIONS FOR THE RADIAL ORNSTEIN-UHLENBECK PROCESSES[J]. Acta mathematica scientia, Series B, 2008 , 28(3) : 513 -522 . DOI: 10.1016/S0252-9602(08)60053-3

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