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Optimal exit probabilities and differential games

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Abstract

The problem considered is to control the drift of a Markov diffusion process in such a way that the probability that the process exits from a given regionD during a given finite time interval is minimum. An asymptotic formula for the minimum exit probability when the process is nearly deterministic is given. This formula involves the lower value of an associated differential game. It is related to a result of Ventsel and Freidlin for nearly deterministic, uncontrolled diffusions.

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Authors and Affiliations

  1. Lefschetz Center for Dynamical Systems, Division of Applied Mathematics, Brown University, 02912, Providence, RI, USA

    Wendell H. Fleming

  2. Department of Mathematics, University of Oklahoma, 73019, Norman, Oklahoma, USA

    Chun-Ping Tsai

Authors
  1. Wendell H. Fleming
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  2. Chun-Ping Tsai
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Additional information

Communicated by A. V. Balakrishnan

This research was supported in part by the Air Force Office of Scientific Research under AF-AFOSR 76-3063C and in part by the National Science Foundation, NSF-76-07261.

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Fleming, W.H., Tsai, CP. Optimal exit probabilities and differential games. Appl Math Optim 7, 253–282 (1981). https://doi.org/10.1007/BF01442120

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  • DOI: https://doi.org/10.1007/BF01442120

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