The stochastic Hamilton-Jacobi equation

@misc{citeulike:2895999, abstract = {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.}, author = {L\&\#xe1;zaro-Cam\&\#xed;, Joan-Andreu and Ortega, Juan-Pablo }, citeulike-article-id = {2895999}, eprint = {0806.0993}, keywords = {hamilton-jacobi, stochastic}, month = {Jun}, posted-at = {2008-06-15 10:20:12}, priority = {2}, title = {The stochastic Hamilton-Jacobi equation}, url = {http://arxiv.org/abs/0806.0993}, year = {2008} }

TY - ELEC ID - citeulike:2895999 L3 - citeulike-article-id:2895999 TI - The stochastic Hamilton-Jacobi equation N2 - 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. KW - hamilton-jacobi KW - stochastic AU - Lázaro-Camí, Joan-Andreu AU - Ortega, Juan-Pablo PY - 2008/Jun/05/ UR - http://arxiv.org/abs/0806.0993 ER -