Q-processes and asymptotic properties of Markov processes conditioned not to hit moving boundaries

STOCHASTIC PROCESSES AND THEIR APPLICATIONS

卷:130

Article

Ocafrain, William¹ 

[1] Univ Toulouse, UMR 5219, Inst Math Toulouse, CNRS,UPS IMT, F-31062 Toulouse 9, France

关键词: Q-process;    Quasi-limiting distribution;    Quasi-ergodic distribution;    Moving boundaries;    One-dimensional diffusion processes;   

DOI  :  10.1016/j.spa.2019.09.019

来源: Elsevier

【 摘 要 】

We investigate some asymptotic properties of general Markov processes conditioned not to be absorbed by the moving boundaries. We first give general criteria involving an exponential convergence towards the Q-process, that is the law of the considered Markov process conditioned never to reach the moving boundaries. This exponential convergence allows us to state the existence and uniqueness of the quasi-ergodic distribution considering either boundaries moving periodically or stabilizing boundaries. We also state the existence and uniqueness of a quasi-limiting distribution when absorbing boundaries stabilize. We finally deal with some examples such as diffusions which are coming down from infinity. (C) 2020 Elsevier B.V. All rights reserved.

【 授权许可】

Free