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2019 Random field solutions to linear SPDEs driven by symmetric pure jump Lévy space-time white noises
Robert C. Dalang, Thomas Humeau
Electron. J. Probab. 24: 1-28 (2019). DOI: 10.1214/19-EJP317

Abstract

We study the notions of mild solution and generalized solution to a linear stochastic partial differential equation driven by a pure jump symmetric Lévy white noise, with symmetric $\alpha $-stable Lévy white noise as an important special case. We identify conditions for existence of these two kinds of solutions, and, together with a new stochastic Fubini theorem, we provide conditions under which they are essentially equivalent. We apply these results to the linear stochastic heat, wave and Poisson equations driven by a symmetric $\alpha $-stable Lévy white noise.

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Robert C. Dalang. Thomas Humeau. "Random field solutions to linear SPDEs driven by symmetric pure jump Lévy space-time white noises." Electron. J. Probab. 24 1 - 28, 2019. https://doi.org/10.1214/19-EJP317

Information

Received: 14 September 2018; Accepted: 7 May 2019; Published: 2019
First available in Project Euclid: 21 June 2019

zbMATH: 07088998
Digital Object Identifier: 10.1214/19-EJP317

Subjects:
Primary: 60H15
Secondary: 60G51, 60G60

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