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arXiv · 2002.05348

A variational characterization of the optimal exit rate for controlled diffusions

Ari Arapostathis·Vivek S. Borkar
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Abstract

The main result in this paper is a variational formula for the exit rate from a bounded domain for a diffusion process in terms of the stationary law of the diffusion constrained to remain in this domain forever. Related results on the geometric ergodicity of the controlled Q-process are also presented.

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Ari Arapostathis, Vivek S. Borkar. 2020-02-13. A variational characterization of the optimal exit rate for controlled diffusions. https://arxiv.org/abs/2002.05348

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