On the geometry of the Hamilton-Jacobi-Bellman equation
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.
Received: October 2008; Revised: June 2009; Available Online: November 2009.
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