A variational characterization of the optimal exit rate for controlled diffusions

2020/02/13 by Arapostathis, Ari, Borkar, Vivek S.
#49G05 #60J25 #60J60 #FOS: Mathematics #Optimization and Control (math.OC) #Probability (math.PR)

paper · doi:10.48550/arxiv.2002.05348

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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