An approximate solution of a case of perturbed Fokker-Planck equation

TL;DR

This paper develops an approximate solution method for a perturbed Fokker-Planck equation with time-dependent factors, proving its existence and linking it to Hamiltonian dynamics to better understand related stochastic systems.

Contribution

It introduces a novel approximate solution formulation for a class of perturbed Fokker-Planck equations and proves its existence, enhancing understanding of these stochastic systems.

Findings

Existence of the approximate solution is rigorously proved.

The formulation is linked to Hamiltonian dynamical systems.

Provides insights into the behavior of systems governed by the perturbed Fokker-Planck equation.

Abstract

This paper focuses on finding an approximate solution of a kind of Fokker-Planck equation with time-dependent perturbations. A formulation of the approximate solution of the equation is constructed, and then the existence of the formulation is proved. The related Hamiltonian dynamical system explains the estimations. Our work provides a more comprehensive understanding of the behaviour of systems described by this Fokker-Planck equation and the corresponding stochastic differential equation.