Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The stochastic Hamilton-Jacobi equation   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.

30
The categories of this paper are: q-alg
13
The categories of this paper are: quant-ph
24
The categories of this paper are: dg-ga
7
The categories of this paper are: hep-th
35
The categories of this paper are: mtrl-th
32
The categories of this paper are: atom-ph
11
The categories of this paper are: hep-lat
4
The categories of this paper are: cond-mat
19
The categories of this paper are: eess
20
The categories of this paper are: acc-phys
22
The categories of this paper are: chao-dyn
29
The categories of this paper are: funct-an
33
The categories of this paper are: plasm-ph
16
The categories of this paper are: stat
18
The categories of this paper are: econ
26
The categories of this paper are: bayes-an