Electronic Journal of Probability
- Electron. J. Probab.
- Volume 24 (2019), paper no. 60, 28 pp.
Random field solutions to linear SPDEs driven by symmetric pure jump Lévy 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 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.
Electron. J. Probab., Volume 24 (2019), paper no. 60, 28 pp.
Received: 14 September 2018
Accepted: 7 May 2019
First available in Project Euclid: 21 June 2019
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Dalang, Robert C.; Humeau, Thomas. Random field solutions to linear SPDEs driven by symmetric pure jump Lévy space-time white noises. Electron. J. Probab. 24 (2019), paper no. 60, 28 pp. doi:10.1214/19-EJP317. https://projecteuclid.org/euclid.ejp/1561082669