Correlated continuous time random walks and fractional Pearson diffusions
Probability
2017-08-24 v1
Abstract
Continuous time random walks have random waiting times between particle jumps. We define the correlated continuous time random walks (CTRWs) that converge to fractional Pearson diffusions (fPDs). The jumps in these CTRWs are obtained from Markov chains through the Bernoulli urn-scheme model and Wright-Fisher model. The jumps are correlated so that the limiting processes are not L\'evy but diffusion processes with non-independent increments. The waiting times are selected from the domain of attraction of a stable law
Cite
@article{arxiv.1708.07086,
title = {Correlated continuous time random walks and fractional Pearson diffusions},
author = {Nikolai N. Leonenko and Ivan Papić and Alla Sikorskii and Nenad Šuvak},
journal= {arXiv preprint arXiv:1708.07086},
year = {2017}
}