Open Access
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


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.


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

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

Keywords: exterior boundary conditions , Feller semigroup , space-time coupled evolution equation , Subordination

Vol.25 • 2020
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