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arXiv · 2103.08534

Degenerate processes killed at the boundary of a domain

Michel Benaïm·Nicolas Champagnat·William Oçafrain·Denis Villemonais
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Abstract

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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Michel Benaïm, Nicolas Champagnat, William Oçafrain, Denis Villemonais. 2021-03-15. Degenerate processes killed at the boundary of a domain. https://arxiv.org/abs/2103.08534

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