Applied Mathematics and Optimization

, Volume 4, Issue 1, pp 329–346 | Cite as

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.


Differential Equation System Theory Diffusion Process Mathematical Method Control Theory 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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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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