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

R. Filliger (), M.-O. Hongler and L. Streit
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R. Filliger: Universidade da Madeira
M.-O. Hongler: Ecole Polytechnique Fédérale de Lausanne
L. Streit: Universidade da Madeira

Journal of Optimization Theory and Applications, 2008, vol. 137, issue 3, No 3, 497-505

Abstract: 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.

Keywords: Optimal stochastic control; Exactly solvable dynamic models; Logarithmic transformations; Reaction-diffusion equations (search for similar items in EconPapers)
Date: 2008
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Citations: View citations in EconPapers (2)

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DOI: 10.1007/s10957-007-9346-2

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