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

We study the notions of mild solution and generalized solution to a linear stochastic partial differential equation driven by a pure jump symmetric Levy white noise, with symmetric alpha-stable Levy 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 Levy white noise.


Published in:
Electronic Journal Of Probability, 24, 1-28
Year:
Jan 01 2019
Publisher:
Seattle, UNIV WASHINGTON, DEPT MATHEMATICS
ISSN:
1083-6489
Keywords:
Laboratories:




 Record created 2019-07-07, last modified 2019-12-05


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