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Degenerate processes killed at the boundary of a domain

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arxiv 2103.08534 v4 pith:OPG5WKSH submitted 2021-03-15 math.PR

Michel Benaïm , Nicolas Champagnat , William Oçafrain , Denis Villemonais This is my paper · ORCID
classification math.PR
keywords conditionsdegenerateensuringkilledprocessesappliedboundarycertain
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We investigate certain properties of degenerate Feller processes that are killed when exiting a relatively compact set. Our main result provides general conditions ensuring that such a process possesses a (possibly non unique) quasi stationary distribution. Conditions ensuring uniqueness and exponential convergence are discussed. The results are applied to nonelliptic and hypoelliptic stochastic differential equations.

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  1. Large deviations of the empirical measures of a strong-Feller Markov process inside a subset and quasi-ergodic distribution

    math.PR 2024-11 conditional novelty 7.0 of 10

    For strong-Feller Markov processes killed on exiting a domain, the occupation measure conditioned on survival obeys a large deviation principle with unique rate-function zero at the quasi-ergodic distribution.

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