Stochastic solution of fractional Fokker-Planck equations with space-time-dependent coefficients

DOI10.1016/j.jmaa.2016.03.033zbMath1342.60106arXiv1510.02113OpenAlexW2963467889MaRDI QIDQ281856

Erkan Nane, Yinan Ni

Publication date: 11 May 2016

Published in: Journal of Mathematical Analysis and Applications (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1510.02113

zbMATH Keywords

Lévy processesfractional Fokker-Planck equationssubdiffusionspace-time-dependent coefficientsstochastic solutions

Mathematics Subject Classification ID

Processes with independent increments; Lévy processes (60G51) Applications of stochastic analysis (to PDEs, etc.) (60H30) Fractional partial differential equations (35R11) Fokker-Planck equations (35Q84)

Related Items

Strong approximation of stochastic differential equations driven by a time-changed Brownian motion with time-space-dependent coefficients, An averaging principle for stochastic differential delay equations driven by time-changed Lévy noise, Heavy-tailed fractional Pearson diffusions, Ergodic properties of Lévy flights coexisting with subdiffusion and related models, On a class of distribution dependent stochastic differential equations driven by time-changed Brownian motions, Stability of the solution of stochastic differential equation driven by time-changed Lévy noise, The local and global existence of solutions for a time fractional complex Ginzburg-Landau equation, Fokker–Planck and Kolmogorov backward equations for continuous time random walk scaling limits, Stability of stochastic differential equations driven by the time-changed Lévy process with impulsive effects, A time-changed stochastic control problem and its maximum principle theory

Cites Work

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• Numerical solutions of a fractional predator-prey system
• Stochastic representation of subdiffusion processes with time-dependent drift
• Particle tracking for fractional diffusion with two time scales
• The Euler scheme for Lévy driven stochastic differential equations
• Comment on fractional Fokker-Planck equation with space and time dependent drift and diffusion
• Fractional Cauchy problems on bounded domains
• Langevin picture of subdiffusion with infinitely divisible waiting times
• Distributed-order fractional diffusions on bounded domains
• Stochastic representation of a fractional subdiffusion equation. The case of infinitely divisible waiting times, Lévy noise and space-time-dependent coefficients
• Comment on “Fokker-Planck equations for nonlinear dynamical systems driven by non-Gaussian Lévy processes” [J. Math. Phys. 53, 072701 (2012)]
• Fokker-Planck equations for nonlinear dynamical systems driven by non-Gaussian Lévy processes
• Lévy Processes and Stochastic Calculus
• Transient anomalous sub-diffusion on bounded domains
• Fractional Langevin equation with α-stable noise. A link to fractional ARIMA time series
• Strong analytic solutions of fractional Cauchy problems
• Stochastic models for fractional calculus
• The random walk's guide to anomalous diffusion: A fractional dynamics approach