Applied Mathematics and Optimization

, Volume 4, Issue 1, pp 329–346

Exit probabilities and optimal stochastic control

  • Wendell H. Fleming


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.


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Copyright information

© Springer-Verlag New York, Inc 1978

Authors and Affiliations

  • Wendell H. Fleming
    • 1
    • 2
  1. 1.Department of MathematicsBrown UniversityProvidenceUSA
  2. 2.Lefschetz Center for Dynamical Systems, Division of Applied MathematicsBrown UniversityProvidenceUSA

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