The stochastic Hamilton-Jacobi equation
Open Access
- 1 January 2009
- journal article
- research article
- Published by American Institute of Mathematical Sciences (AIMS) in Journal of Geometric Mechanics
- Vol. 1 (3), 295-315
- https://doi.org/10.3934/jgm.2009.1.295
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.Keywords
Other Versions
This publication has 2 references indexed in Scilit:
- Stochastic variational integratorsIMA Journal of Numerical Analysis, 2008
- Stochastic hamiltonian dynamical systemsReports on Mathematical Physics, 2008