Non-local in time telegraph equations and very slowly growing variances
Analysis of PDEs
2021-01-20 v1 Probability
Abstract
In this paper we consider a class of non-local in time telegraph equations. Recently, it has been proved that the fundamental solutions of such equations can be interpreted as the probability density function of a stochastic process. We study the asymptotic behavior of the variance of this process at large and short times. In this context, we develop a method to construct new examples such the variance has a slowly growth behavior, extending the earlier results. Finally, we show that our approach can be adapted to define new integro-differential operators which are interesting in sub-diffusion processes.
Keywords
Cite
@article{arxiv.2101.07323,
title = {Non-local in time telegraph equations and very slowly growing variances},
author = {Francisco Alegría and Juan C. Pozo},
journal= {arXiv preprint arXiv:2101.07323},
year = {2021}
}