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The Journal of Geometric Mechanics (JGM)
 

On the geometry of the Hamilton-Jacobi-Bellman equation

Pages: 369 - 387, Volume 1, Issue 3, September 2009      doi:10.3934/jgm.2009.1.369

 
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Jean-Claude Zambrini - Grupo de Física-Matemática da Universidade de Lisboa, Av. Prof. Gama Pinto, 2, 1649-003 Lisboa, Portugal (email)

Abstract: 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, Hamilton-Jacobi Bellman, Stochastic perturbations of dynamical systems, Noether and stochastic Noether Theorem.
Mathematics Subject Classification:  Primary: 37J05; Secondary: 60H10, 60H30, 60M07.

Received: October 2008;      Revised: June 2009;      Available Online: November 2009.