随机Hamilton-Jacobi方程
The stochastic Hamilton-Jacobi equation
摘要：
我们将Hamilton-Jacobi理论的某些方面推广到随机Hamiltonian动力系统的范畴。更具体地说，我们表明，随机行动满足的Hamilton-Jacobi方程时，在经典的情况下，它被写为一个功能的配置空间使用一个定期的拉格朗日子流形。此外，我们将使用一个变化的哈密顿-雅可比方程的特征的生成函数的一个参数组的symplectomorphisms，允许重写一个给定的随机哈密顿系统的形式，其解决方案是很容易找到的，这一结果恢复在随机背景下的经典解的方法，减少到平衡的哈密顿系统。
英文摘要：
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.
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