Journal of Optimization Theory and Applications

, Volume 137, Issue 3, pp 497–505

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


DOI: 10.1007/s10957-007-9346-2

Cite this article as:
Filliger, R., Hongler, MO. & Streit, L. J Optim Theory Appl (2008) 137: 497. doi:10.1007/s10957-007-9346-2


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.


Optimal stochastic controlExactly solvable dynamic modelsLogarithmic transformationsReaction-diffusion equations

Copyright information

© Springer Science+Business Media, LLC 2007

Authors and Affiliations

  1. 1.CCMUniversidade da MadeiraFunchalPortugal
  2. 2.Institut de Production et RobotiqueEcole Polytechnique Fédérale de LausanneLausanneSwitzerland