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.
This work was funded by grant 200020 196999 from the Swiss National Foundation.
The author would like to thank Michel Benaïm for useful discussions on the convergence (or lack thereof) of reinforced processes, leading in particular to Corollary 2.4. The author also thanks the anonymous referee, whose feedback has improved this paper.
"Stochastic approximation of the paths of killed Markov processes conditioned on survival." Electron. Commun. Probab. 27 1 - 13, 2022. https://doi.org/10.1214/22-ECP475