Fokker–Planck equation and path integral representation of the fractional Ornstein–Uhlenbeck process with two indices

  title={Fokker–Planck equation and path integral representation of the fractional Ornstein–Uhlenbeck process with two indices},
  author={Chai Hok Eab and S. C. Lim},
  journal={Journal of Physics A: Mathematical and Theoretical},
  • C. EabS. C. Lim
  • Published 4 May 2014
  • Mathematics
  • Journal of Physics A: Mathematical and Theoretical
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. The path integral representation of the process is constructed, and the basic quantities are evaluated. 

Some Fractional and Multifractional Gaussian Processes: A Brief Introduction

This paper gives a brief introduction to some important fractional and multifractional Gaussian processes commonly used in modelling natural phenomena and man-made systems. The processes include

The chemical birth-death process with additive noise.

This system is used to showcase eight qualitatively different ways to exactly solve continuous stochastic systems.



Green function of the double-fractional Fokker-Planck equation: path integral and stochastic differential equations.

The statistics of rare events, the so-called black-swan events, is governed by non-Gaussian distributions with heavy power-like tails. We calculate the Green functions of the associated Fokker-Planck

Fokker-Planck-Kolmogorov equations associated with time-changed fractional Brownian motion

In this paper Fokker-Planck-Kolmogorov type equations associated with stochastic differential equations driven by a time-changed fractional Brownian motion are derived. Two equivalent forms are

Weyl and Riemann–Liouville multifractional Ornstein–Uhlenbeck processes

This paper considers two new multifractional stochastic processes, namely the Weyl multifractional Ornstein–Uhlenbeck process and the Riemann–Liouville multifractional Ornstein–Uhlenbeck process.

Generalized Ornstein–Uhlenbeck processes and associated self-similar processes

We consider three types of generalized Ornstein–Uhlenbeck processes: the stationary process obtained from the Lamperti transformation of fractional Brownian motion, the process with stretched

Fractional Ornstein-Uhlenbeck processes

The classical stationary Ornstein-Uhlenbeck process can be obtained in two different ways. On the one hand, it is a stationary solution of the Langevin equation with Brownian motion noise. On the

Fractional Lévy motion through path integrals

Fractional Lévy motion (fLm) is the natural generalization of fractional Brownian motion in the context of self-similar stochastic processes and stable probability distributions. In this paper we

Path Integral Formulation of Anomalous Diffusion Processes

We present the path integral formulation of a broad class of generalized diffusion processes. Employing the path integral we derive exact expressions for the path probability densities and joint