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Stochastic control and large deviations

  • V. Signal Processing, Control, and Manufacturing Automation
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Future Tendencies in Computer Science, Control and Applied Mathematics (INRIA 1992)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 653))

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Abstract

Large deviations theory is concerned with asymptotic estimates of probabilities of rare events associated with stochastic processes. A stochastic control approach to large deviations is outlined. Both problems of small random perturbations and large deviations from ergodicity are considered. For large deviations of Markov diffusion processes, PDE — viscosity solution methods are mentioned. Another stochastic control formulation, applicable to a broad range of large deviations problems is due to Dupuis and Ellis. This approach reduces many aspects of large deviations to the theory of weak convergence of probability measures.

Partially supported by NSF under grant DMS-900038, by AFOSR under grant F49620-92-J-0081DEF and by ARO under grant DAAL03-86-K-0171

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Authors and Affiliations

  1. Division of Applied Mathematics, Brown University, 02912, Providence, RI

    Wendell H. Fleming

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  1. Wendell H. Fleming
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A. Bensoussan J. -P. Verjus

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© 1992 Springer-Verlag Berlin Heidelberg

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Fleming, W.H. (1992). Stochastic control and large deviations. In: Bensoussan, A., Verjus, J.P. (eds) Future Tendencies in Computer Science, Control and Applied Mathematics. INRIA 1992. Lecture Notes in Computer Science, vol 653. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-56320-2_66

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  • DOI: https://doi.org/10.1007/3-540-56320-2_66

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  • Print ISBN: 978-3-540-56320-4

  • Online ISBN: 978-3-540-47520-0

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