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Stochastic control for a class of random evolution models

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Hongler, Max-Olivier
Streit, Ludwig

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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.

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Springer-Verlag

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Mathematics

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Applied Mathematics and Optimization

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10.1007/s00245-003-0786-2

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