Exit Probabilities and Optimal Stochastic Control.
BROWN UNIV PROVIDENCE R I LEFSCHETZ CENTER FOR DYNAMICAL SYSTEMS
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This paper is concerned with Markov diffusion processes which obey stochastic differential equations depending on a small parameter E. The parameter enters as a coefficient in the noise term of the stochastic differential equation. The Ventcel-Freidlin estimates give asymptotic formulas as E approaches 0 for such quantities as the probability of exit from a region D through a given portion N of the boundary increment of D, the mean exit time, and the probability of exit by a given time T. A new method to obtain such estimates is given, using ideas from stochastic control theory.
- Statistics and Probability