Applied Mathematics and Optimization

, Volume 49, Issue 2, pp 159–181 | Cite as

Max-plus stochastic processes

  • Wendell H. Fleming
Article
Accepted:

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.

Key Words

Max-plus probability Stochastic differential equations Max-plus additive functionals Variational inequalities 

AMS Classification

35F20 60H10 93E20 
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Copyright information

© Springer-Verlag New York Inc 2004

Authors and Affiliations

  • Wendell H. Fleming
    • 1
  1. 1.Division of Applied Mathematics and Lefschetz Center for Dynamical SystemsBrown UniversityProvidenceUSA

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