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Connection between an Exactly Solvable Stochastic Optimal Control Problem and a Nonlinear Reaction-Diffusion Equation

Author

Listed:
  • R. Filliger

    (Universidade da Madeira)

  • M.-O. Hongler

    (Ecole Polytechnique Fédérale de Lausanne)

  • L. Streit

    (Universidade da Madeira)

Abstract

We present an exactly soluble optimal stochastic control problem involving a diffusive two-states random evolution process and connect it to a nonlinear reaction-diffusion type of equation by using the technique of logarithmic transformations. The work generalizes the recently established connection between the non-linear Boltzmann-like equations introduced by Ruijgrok and Wu and the optimal control of a two-states random evolution process. In the sense of this generalization, the nonlinear reaction-diffusion equation is identified as the natural diffusive generalization of the Ruijgrok–Wu and Boltzmann model.

Suggested Citation

  • R. Filliger & M.-O. Hongler & L. Streit, 2008. "Connection between an Exactly Solvable Stochastic Optimal Control Problem and a Nonlinear Reaction-Diffusion Equation," Journal of Optimization Theory and Applications, Springer, vol. 137(3), pages 497-505, June.
    • Handle: RePEc:spr:joptap:v:137:y:2008:i:3:d:10.1007_s10957-007-9346-2
    DOI: 10.1007/s10957-007-9346-2
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    References listed on IDEAS

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    1. Ruijgrok, Th.W. & Wu, Tai Tsun, 1982. "A completely solvable model of the nonlinear Boltzmann equation," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 113(3), pages 401-416.
    2. Masoliver, Jaume & Lindenberg, Katja & Weiss, George H., 1989. "A continuous-time generalization of the persistent random walk," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 157(2), pages 891-898.
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    Cited by:

    1. Aníbal Coronel & Fernando Huancas & Esperanza Lozada & Marko Rojas-Medar, 2021. "The Dubovitskii and Milyutin Methodology Applied to an Optimal Control Problem Originating in an Ecological System," Mathematics, MDPI, vol. 9(5), pages 1-17, February.
    2. Yongxin Chen & Tryphon T. Georgiou & Michele Pavon, 2016. "On the Relation Between Optimal Transport and Schrödinger Bridges: A Stochastic Control Viewpoint," Journal of Optimization Theory and Applications, Springer, vol. 169(2), pages 671-691, May.

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