Space-time coupled evolution equations and their stochastic solutions
Analysis of PDEs
2019-03-12 v1 Probability
Abstract
We consider a class of space-time coupled evolution equations (CEEs), obtained by a subordination of the heat operator. Our CEEs reformulate and extend known governing equations of non-Markovian processes arising as scaling limits of continuous time random walks, with widespread applications. In particular we allow for initial conditions imposed on the past, general spatial operators on Euclidean domains and a forcing term. We prove existence, uniqueness and stochastic representation for solutions.
Cite
@article{arxiv.1903.04052,
title = {Space-time coupled evolution equations and their stochastic solutions},
author = {John Herman and Ifan Johnston and Lorenzo Toniazzi},
journal= {arXiv preprint arXiv:1903.04052},
year = {2019}
}
Comments
24 pages; submitted for publication