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

William Oçafrain

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arXiv · 1803.06145

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

William Oçafrain

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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.

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William Oçafrain. 2018-03-16. Q-processes and asymptotic properties of Markov processes conditioned not to hit moving boundaries. https://arxiv.org/abs/1803.06145

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