, Volume 4, Issue 1, pp 329-346

Exit probabilities and optimal stochastic control

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Abstract

This paper is concerned with Markov diffusion processes which obey stochastic differential equations depending on a small parameterε. The parameter enters as a coefficient in the noise term of the stochastic differential equation. The Ventcel-Freidlin estimates give asymptotic formulas (asε→0) for such quantities as the probability of exit from a regionD through a given portionN of the boundary ∂D, the mean exit time, and the probability of exit by a given timeT. A new method to obtain such estimates is given, using ideas from stochastic control theory.

This research was supported by the Air Force Office of Scientific Research under AF-AFOSR 76-3063, and in part by the National Science Foundation under NSF-MCS 76-37247.