Applied Mathematics and Optimization

, Volume 49, Issue 2, pp 113–121

Stochastic control for a class of random evolution models

  • Max-Olivier Hongler
  • Halil Mete Soner
  • Ludwig Streit

DOI: 10.1007/BF02638147

Cite this article as:
Hongler, MO., Soner, H.M. & Streit, L. Appl Math Optim (2004) 49: 113. doi:10.1007/BF02638147


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.

Key Words

Piecewise deterministic evolutions Stochastic optimal control Logarithmic transformation Nonlinear field equations 

AMS Classification

60G40 93C10 

Copyright information

© Springer-Verlag New York Inc 2004

Authors and Affiliations

  • Max-Olivier Hongler
    • 1
  • Halil Mete Soner
    • 2
  • Ludwig Streit
    • 3
    • 4
  1. 1.Institut de Production et Robotique/(LPM)Ecole Polytechnique Fédérale de LausanneLausanneSwitzerland
  2. 2.Department of MathematicsKoc UniversityIstanbulTurkey
  3. 3.CCM-Centro de Ciencias MatematicasUniversidade da MadeiraFunchalPortugal
  4. 4.BiBoS, University of BielefeldBielefeldGermany

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