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2020 Space-time coupled evolution equations and their stochastic solutions
John Herman, Ifan Johnston, Lorenzo Toniazzi
Electron. J. Probab. 25: 1-21 (2020). DOI: 10.1214/20-EJP544

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.

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John Herman. Ifan Johnston. Lorenzo Toniazzi. "Space-time coupled evolution equations and their stochastic solutions." Electron. J. Probab. 25 1 - 21, 2020. https://doi.org/10.1214/20-EJP544

Information

Received: 10 March 2019; Accepted: 5 November 2020; Published: 2020
First available in Project Euclid: 19 December 2020

Digital Object Identifier: 10.1214/20-EJP544

Subjects:
Primary: 35C15, 35R11, 45K05, 60H30

JOURNAL ARTICLE
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Vol.25 • 2020
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