Existence and construction of quasi-stationary distributions for one-dimensional diffusions

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:434

Article

Zhang, Hanjun¹  He, Guoman¹ 

[1] Xiangtan Univ, Sch Math & Computat Sci, Xiangtan 411105, Hunan, Peoples R China

关键词: One-dimensional diffusion;    Quasi-stationary distribution;    R-positivity;    Natural boundary;   

DOI  :  10.1016/j.jmaa.2015.09.010

来源: Elsevier

【 摘 要 】

In this paper, we study quasi-stationary distributions (QSDs) for one-dimensional diffusions killed at 0, when 0 is a regular boundary and +infinity is a natural boundary. More precisely, we not only give a necessary and sufficient condition for the existence of a QSD, but we also construct all QSDs for the one-dimensional diffusions. Moreover, we give a sufficient condition for R-positivity of the process killed at the origin. This condition is only based on the drift, which is easy to check. (C) 2015 Elsevier Inc. All rights reserved.

【 授权许可】

Free