Dresden 2006 – scientific programme

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DY: Dynamik und Statistische Physik

DY 21: Statistical Physics (general) I

DY 21.7: Talk

Tuesday, March 28, 2006, 11:30–11:45, SCH 251

A connection between an exactly soluble stochastic control problem and a nonlinear reaction-diffusion equation — •Roger Filliger¹, Max Olivier Hongler², and Ludwig Streit¹ — ¹CCM, Universidade da Madeira, Portugal — ²IPR, EPF-Lausanne, Switzerland

We present an exactly soluble optimal stochastic control problem involving a diffusive two-state random evolution process and connect it to a non-linear reaction-diffusion type of equation by using the technique of logarithmic transformations. The work generalizes the recently established connection between a discrete two velocities, non-linear Boltzmann equation and the optimal control of a two-state random evolution process. We further show that the cost structure associated to the control problem is connected to the large deviations probabilities of the uncontrolled dynamics.