Connection between an Exactly Solvable Stochastic Optimal Control Problem and a Nonlinear Reaction-Diffusion Equation
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- Filliger, R., Hongler, MO. & Streit, L. J Optim Theory Appl (2008) 137: 497. doi:10.1007/s10957-007-9346-2
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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.