Random field solutions to linear SPDEs driven by symmetric pure jump Lévy space-time white noises

2018/09/26 by Dalang, Robert C., Humeau, Thomas · 1 citation
#60G51 (Secondary) #60G60 #60H15 (Primary) #FOS: Mathematics #Probability (math.PR)

paper · doi:10.48550/arxiv.1809.09999

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. We identify conditions for existence for these two kinds of solutions, and we identify conditions under which they are essentially equivalent. We establish a necessary condition for the existence of a random field solution to a linear SPDE, and we apply this result to the linear stochastic heat, wave and Poisson equations driven by a symmetric α-stable noise.

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• Pathwise regularity of solutions for a class of elliptic SPDEs with symmetric Lévy noise

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