Stochastic representation of a fractional subdiffusion equation. The case of infinitely divisible waiting times, Lévy noise and space-time-dependent coefficients

DOI10.1090/proc/12856zbMath1335.60126arXiv1509.09051OpenAlexW2962687925MaRDI QIDQ2790283

Marcin Magdziarz, Tomasz Zorawik

Publication date: 3 March 2016

Published in: Proceedings of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1509.09051

zbMATH Keywords

Brownian motionLangevin equationMonte Carlo methodsFokker-Planck-Kolmogorov equationLévy noisefractional subdiffusion equationfractional subdivision

Mathematics Subject Classification ID

Processes with independent increments; Lévy processes (60G51) Fractional processes, including fractional Brownian motion (60G22) Monte Carlo methods (65C05) Stochastic ordinary differential equations (aspects of stochastic analysis) (60H10) Brownian motion (60J65) Applications of stochastic analysis (to PDEs, etc.) (60H30) Diffusion processes (60J60) Fractional partial differential equations (35R11) Fokker-Planck equations (35Q84)

Related Items (13)

Stochastic solution of fractional Fokker-Planck equations with space-time-dependent coefficients ⋮ Strong approximation of stochastic differential equations driven by a time-changed Brownian motion with time-space-dependent coefficients ⋮ Asymptotic degeneracy and subdiffusivity ⋮ Mittag-Leffler function and fractional differential equations ⋮ Heavy-tailed fractional Pearson diffusions ⋮ Ergodic properties of Lévy flights coexisting with subdiffusion and related models ⋮ Spectral heat content for time-changed killed Brownian motions ⋮ Solving Multidimensional Fractional Fokker--Planck Equations via Unbiased Density Formulas for Anomalous Diffusion Processes ⋮ Comment on “Fokker-Planck equations for nonlinear dynamical systems driven by non-Gaussian Lévy processes” [J. Math. Phys. 53, 072701 (2012)] ⋮ Cusping, transport and variance of solutions to generalized Fokker–Planck equations ⋮ Reaction-Subdiffusion Equations with Species-Dependent Movement ⋮ Extreme statistics of anomalous subdiffusion following a fractional Fokker–Planck equation: subdiffusion is faster than normal diffusion ⋮ A time-changed stochastic control problem and its maximum principle theory

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