Max-plus stochastic processes

被引：17
|
作者：
Fleming, WH [1 ]
机构：
[1] Brown Univ, Div Appl Math, Providence, RI 02912 USA
[2] Brown Univ, Lefschetz Ctr Dynam Syst, Providence, RI 02912 USA
来源：
APPLIED MATHEMATICS AND OPTIMIZATION | 2004年 / 49卷 / 02期
关键词：
max-plus probability; stochastic differential equations; max-plus additive functionals; variational inequalities;
D O I：
10.1007/s00245-003-0785-3
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
This paper is concerned with processes which are max-plus counterparts 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.
引用
收藏
页码：159 / 181
页数：23
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