Stochastic control for a class of random evolution models

Stochastic control for a class of random evolution models 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. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Applied Mathematics and Optimization Springer Journals

Stochastic control for a class of random evolution models

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Publisher
Springer-Verlag
Copyright
Copyright © 2004 by Springer-Verlag
Subject
Mathematics; Systems Theory, Control; Calculus of Variations and Optimal Control; Optimization; Mathematical and Computational Physics; Mathematical Methods in Physics; Numerical and Computational Methods
ISSN
0095-4616
eISSN
1432-0606
D.O.I.
10.1007/BF02638147
Publisher site
See Article on Publisher Site

Abstract

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.

Journal

Applied Mathematics and OptimizationSpringer Journals

Published: Apr 1, 2004

References

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