Fractional Fokker--Planck Equation for Nonlinear Stochastic Differential Equations Driven by Non-Gaussian Levy Stable Noises

Abstract

The Fokker-Planck equation has been very useful for studying dynamic behavior of stochastic differential equations driven by Gaussian noises. In this paper, we derive a Fractional Fokker--Planck equation for the probability distribution of particles whose motion is governed by a {\em nonlinear} Langevin-type equation, which is driven by a non-Gaussian Levy-stable noise. We obtain in fact a more general result for Markovian processes generated by stochastic differential equations.}

References in corpus (2)

• Langevin equations for continuous time Lévy flights
• Levy Anomalous Diffusion and Fractional Fokker--Planck Equation

Cited by in corpus (63)

• Levy Flight Superdiffusion: An Introduction
• The growth equation of cities
• Escape driven by $\alpha$-stable white noises
• Joint Probability Distributions for a Class of Non-Markovian Processes
• Saturation and Scaling of Multiplicity, Mean p_T and p_T Distributions from 200 GeV < sqrt{s} < 7 TeV - Addendum
• Stationary states in Langevin dynamics under asymmetric Lévy noises
• SDEs driven by a time-changed Lévy process and their associated time-fractional order pseudo-differential equations
• Transport in a Levy ratchet: Group velocity and distribution spread
• Fractional Fokker-Planck equation for Lévy flights in nonhomogeneous environments
• Multiplicative Lévy processes: Itô versus Stratonovich interpretation
• Finite size scaling in the solar wind magnetic field energy density as seen by WIND
• Mean exit time and escape probability for the anomalous processes with the tempered power-law waiting times
• Stationary states in single-well potentials under symmetric Levy noises
• Subdiffusion in an external force field
• Tempered fractional Langevin-Brownian motion with inverse $\beta$-stable subordinator
• Fokker-Planck equations for nonlinear dynamical systems driven by non-Gaussian Levy processes
• Lévy-noise versus Gaussian-noise-induced Transitions in the Ghil-Sellers Energy Balance Model
• Anomalous diffusion in systems driven by the stable Levy noise with a finite noise relaxation time and inertia
• Ergodic property of random diffusivity system with trapping events
• Heat and work distributions for mixed Gauss-Cauchy process
• Influence of external potentials on heterogeneous diffusion processes
• Extended Anderson Criticality in Heavy-Tailed Neural Networks
• Multiplicative Levy noise in bistable systems
• Lévy noise-driven escape from arctan potential wells
• Continuous time multidimensional Markovian description of Levy walks
• Dynamical Inference for Transitions in Stochastic Systems with $\alpha -$stable Lévy Noise
• Anomalous diffusion in nonhomogeneous media: Time-subordinated Langevin equation approach
• Lévy flights in inhomogeneous environments and 1/f noise
• Diffusion of Active Particles With Stochastic Torques Modeled as $\alpha$-Stable Noise
• Multimodal stationary states in symmetric single-well potentials driven by Cauchy noise
• Escape from bounded domains driven by multi-variate $\alpha$-stable noises
• Stationary states in 2D systems driven by bi-variate Lévy noises
• Extracting Non-Gaussian Governing Laws from Data on Mean Exit Time
• Bimodality and hysteresis in systems driven by confined Lévy flights
• Multimodal stationary states under Cauchy noise
• Fluctuations in multiplicative systems with jumps
• 1/f noise from point process and time-subordinated Langevin equations
• Optimal Noise in a Stochastic Model for Local Search
• Escape from the potential well: competition between long jumps and long waiting times
• Peculiarities of escape kinetics in the presence of athermal noises
• Phase transitions driven by Lévy stable noise: exact solutions and stability analysis of nonlinear fractional Fokker-Planck equations
• Target Search of a Protein on DNA in the Presence of Position-dependent Bias
• Stationary states for underdamped anharmonic oscillators driven by Cauchy noise
• Dynamical behavior of a nonlocal Fokker-Planck equation for a stochastic system with tempered stable noise
• Search and Return Model for Stochastic Path Integrators
• Anomalous diffusion in stochastic systems with nonhomogeneously distributed traps
• Probability distribution function for systems driven by superheavy-tailed noise
• Adiabatic elimination of inertia of the stochastic microswimmer driven by $\alpha -$stable noise
• Asymmetric Levy flights in nonhomogeneous environments
• Quantifying resonant activation like phenomenon in non-Markovian systems
• Maximum principles for nonlocal parabolic Waldenfels operators
• Random walk in nonhomogeneous environments: A possible approach to human and animal mobility
• The neutral heavy scalar productions associated with $Z_L$ in the littlest Higgs model at ILC and CLIC
• Equivalent continuous and discrete realizations of Levy flights: Model of one-dimensional motion of inertial particle
• Nonlinear friction in underdamped anharmonic stochastic oscillators
• Resetting induced multimodality
• Stochastic equations and cities
• Role of long jumps in Lévy noise induced multimodality
• Kolmogorov Modes and Linear Response of Jump-Diffusion Models
• Eigenvalues and eigenvectors of the Laplace operator in d-dimensional cut Fock basis
• Resonant activation in 2D and 3D systems driven by multi-variate Lévy noises
• Stochastic kinetics under combined action of two noise sources
• Drifted escape from the finite interval