Fokker--Planck and Kolmogorov Backward Equations for Continuous Time Random Walk scaling limits

Abstract

It is proved that the distributions of scaling limits of Continuous Time Random Walks (CTRWs) solve integro-differential equations akin to Fokker-Planck Equations for diffusion processes. In contrast to previous such results, it is not assumed that the underlying process has absolutely continuous laws. Moreover, governing equations in the backward variables are derived. Three examples of anomalous diffusion processes illustrate the theory.

in Proceedings of the American Mathematical Society, Published electronically July 12, 2016

References in corpus (3)

• Fractional Fokker-Planck Equations for Subdiffusion with Space-and-Time-Dependent Forces
• On distributions of functionals of anomalous diffusion paths
• Subdiffusive master equation with space dependent anomalous exponent: `Black Swan' effects

Cited by in corpus (4)

• Variable Order Fractional Fokker-Planck Equations derived from Continuous Time Random Walks
• From semi-Markov random evolutions to scattering transport and superdiffusion
• A Semi-Markov Algorithm for Continuous Time Random Walk Limit Distributions
• Wasserstein Gradient Flow Formulation of the Time-Fractional Fokker-Planck Equation