%0 Journal Article %T The stochastic Hamilton-Jacobi equation %A Joan-Andreu L¨¢zaro-Cam¨ª %A Juan-Pablo Ortega %J Mathematics %D 2008 %I arXiv %X We extend some aspects of the Hamilton-Jacobi theory to the category of stochastic Hamiltonian dynamical systems. More specifically, we show that the stochastic action satisfies the Hamilton-Jacobi equation when, as in the classical situation, it is written as a function of the configuration space using a regular Lagrangian submanifold. Additionally, we will use a variation of the Hamilton-Jacobi equation to characterize the generating functions of one-parameter groups of symplectomorphisms that allow to rewrite a given stochastic Hamiltonian system in a form whose solutions are very easy to find; this result recovers in the stochastic context the classical solution method by reduction to the equilibrium of a Hamiltonian system. %U http://arxiv.org/abs/0806.0993v2