Stochastic Approximation of the Paths of Killed Markov Processes Conditioned on Survival

Abstract

Reinforced processes are known to provide a stochastic representation for the quasi-stationary distribution of a given killed Markov process - describing the killed Markov process at fixed time instants. In this paper we shall adapt the construction to provide a pathwise description. We also obtain a stochastic approximation for the quasi-limiting distributions of reducible killed Markov processes as a corollary.

arXiv comment12 pages, 1 figure