Existence and uniqueness of a quasi-stationary distribution for Markov processes with fast return from infinity

Details Existence and uniqueness of a quasi-stationary distribution for Markov processes with fast return from infinity Existence and uniqueness of a quasi-stationary distribution for Markov processes with fast return from infinity

2012-02-03

arxiv.org/abs/1202.0677v1

Mathematics

Probability

15 pages

Scientific paper

We consider a Markov process evolving in $\N$ such that 0 is an absorbing point and we study the long time behavior of the distribution of the process conditioned not to be absorbed when it is observed. Our main condition is that the process comes back quickly from infinity to a finite subset of $\N$. In particular, we prove that this conditional distribution admits a limit when the time goes to infinity, and that this limit doesn't depend on the initial distribution of the process. This limiting distribution, usually called a Yaglom limit, will then appear to be the unique quasi-stationary distribution of the process.

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