Fokker-Planck Equation and Path Integral Representation of Fractional Ornstein-Uhlenbeck Process with Two Indices

TL;DR

This paper derives the Fokker-Planck equation and constructs a path integral representation for a fractional Ornstein-Uhlenbeck process characterized by two indices, providing new analytical tools for its analysis.

Contribution

It introduces a novel fractional Ornstein-Uhlenbeck process with two parameters and develops its Fokker-Planck and path integral formulations, expanding the mathematical framework for such processes.

Findings

Derived the effective Fokker-Planck equation from the fractional Langevin equation

Constructed the path integral representation of the process

Evaluated basic quantities within the new framework

Abstract

This paper considers the Fokker-Planck equation and path integral formulation of the fractional Ornstein-Uhlenbeck process parametrized by two indices. The effective Fokker-Planck equation of this process is derived from the associated fractional Langevin equation. Path integral representation of the process is constructed and the basic quantities are evaluated.