Q-processes and asymptotic properties of Markov processes conditioned not to hit moving boundaries
Abstract
We investigate some asymptotic properties of general Markov processes conditioned not to be absorbed by 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 quasi-ergodic distribution considering either boundaries moving periodically or stabilizing boundaries. We also state the existence and uniqueness of quasi-limit distribution when absorbing boundaries stabilize. We finally deal with some examples such as diffusions which are coming down from infinity.
Keywords
Cite
@article{arxiv.1803.06145,
title = {Q-processes and asymptotic properties of Markov processes conditioned not to hit moving boundaries},
author = {William Oçafrain},
journal= {arXiv preprint arXiv:1803.06145},
year = {2020}
}
Comments
Stochastic Processes and their Applications, Elsevier, In press