Max-plus stochastic processes

Max-plus stochastic processes This paper is concerned with processes which are max-plus counter-parts of Markov diffusion processes governed by Ito sense stochastic differential equations. Concepts of max-plus martingale and max-plus stochastic differential equation are introduced. The max-plus counterparts of backward and forward PDEs for Markov diffusions turn out to be first-order PDEs of Hamilton-Jacobi-Bellman type. Max-plus additive integrals and a max-plus additive dynamic programming principle are considered. This leads to variational inequalities of Hamilton-Jacobi-Bellman type. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Applied Mathematics and Optimization Springer Journals

Max-plus stochastic processes

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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/BF02638150
Publisher site
See Article on Publisher Site

Abstract

This paper is concerned with processes which are max-plus counter-parts of Markov diffusion processes governed by Ito sense stochastic differential equations. Concepts of max-plus martingale and max-plus stochastic differential equation are introduced. The max-plus counterparts of backward and forward PDEs for Markov diffusions turn out to be first-order PDEs of Hamilton-Jacobi-Bellman type. Max-plus additive integrals and a max-plus additive dynamic programming principle are considered. This leads to variational inequalities of Hamilton-Jacobi-Bellman type.

Journal

Applied Mathematics and OptimizationSpringer Journals

Published: Apr 1, 2004

References

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