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September  2009, 1(3): 369-387. doi: 10.3934/jgm.2009.1.369

On the geometry of the Hamilton-Jacobi-Bellman equation

Jean-Claude Zambrini 1,

1. 

Grupo de Física-Matemática da Universidade de Lisboa, Av. Prof. Gama Pinto, 2, 1649-003 Lisboa, Portugal

Received  October 2008 Revised  June 2009 Published  November 2009

We show how a minimal deformation of the geometry of the classical Hamilton-Jacobi equation provides a probabilistic theory whose cornerstone is the Hamilton-Jacobi-Bellman equation. This is the basis for a novel dynamical system approach to Stochastic Analysis.
Keywords: Hamilton-Jacobi, Noether and stochastic Noether Theorem., Stochastic perturbations of dynamical systems, Hamilton-Jacobi Bellman.
Mathematics Subject Classification: Primary: 37J05; Secondary: 60H10, 60H30, 60M0.
Citation: Jean-Claude Zambrini. On the geometry of the Hamilton-Jacobi-Bellman equation. Journal of Geometric Mechanics, 2009, 1 (3) : 369-387. doi: 10.3934/jgm.2009.1.369
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