Fokker--Planck and Kolmogorov Backward Equations for Continuous Time Random Walk scaling limits
Probability
2016-07-20 v3
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.
Keywords
Cite
@article{arxiv.1501.00533,
title = {Fokker--Planck and Kolmogorov Backward Equations for Continuous Time Random Walk scaling limits},
author = {Boris Baeumer and Peter Straka},
journal= {arXiv preprint arXiv:1501.00533},
year = {2016}
}
Comments
in Proceedings of the American Mathematical Society, Published electronically July 12, 2016