Open Access
2022 Stochastic approximation of the paths of killed Markov processes conditioned on survival
Oliver Tough
Author Affiliations +
Electron. Commun. Probab. 27: 1-13 (2022). DOI: 10.1214/22-ECP475


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.

Funding Statement

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.


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Oliver Tough. "Stochastic approximation of the paths of killed Markov processes conditioned on survival." Electron. Commun. Probab. 27 1 - 13, 2022.


Received: 9 February 2022; Accepted: 27 June 2022; Published: 2022
First available in Project Euclid: 26 July 2022

MathSciNet: MR4458033
zbMATH: 1511.60108
Digital Object Identifier: 10.1214/22-ECP475

Primary: 60J10 , 60J85

Keywords: killed Markov processes , Reinforced processes , urn processes

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