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Stochastic Control for a Class of Random Evolution Models

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Abstract

We construct the explicit connection existing between a solvable model of the discrete velocities non-linear Boltzmann equation and the Hamilton–Bellman–Jacobi equation associated with a simple optimal control of a piecewise deterministic process. This study extends the known relation that exists between the Burgers equation and a simple controlled diffusion problem. In both cases the resulting partial differential equations can be linearized via a logarithmic transformation and hence offer the possibility to solve physically relevant non-linear field models in full generality.

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Authors and Affiliations

  1. Institut de Production et Robotique / (LPM), Ecole Polytechnique Fédérale de Lausanne, CH-1015 Lausanne, Switzerland

    Max-Olivier Hongler

  2. Department of Mathematics, Koc University, Fener Yolu Caddesi, Sariyer 80910, Istanbul, Turkey

    Halil Mete Soner

  3. CCM-Centro de Ciencias Matematicas, Universidade da Madeira, P-9000 Funchal, Portugal and BiBoS, University of Bielefeld, D-33615 Bielefeld, Germany

    Ludwig Streit

Authors
  1. Max-Olivier Hongler
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  2. Halil Mete Soner
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  3. Ludwig Streit
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Corresponding authors

Correspondence to Max-Olivier Hongler, Halil Mete Soner or Ludwig Streit.

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Hongler, MO., Soner, H. & Streit, L. Stochastic Control for a Class of Random Evolution Models. Appl Math Optim 49, 113–121 (2004). https://doi.org/10.1007/s00245-003-0786-2

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  • DOI: https://doi.org/10.1007/s00245-003-0786-2

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