Electronic Communications in Probability

Stable cylindrical Lévy processes and the stochastic Cauchy problem

Markus Riedle

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In this work, we consider the stochastic Cauchy problem driven by the canonical $\alpha $-stable cylindrical Lévy process. This noise naturally generalises the cylindrical Brownian motion or space-time Gaussian white noise. We derive a sufficient and necessary condition for the existence of the weak and mild solution of the stochastic Cauchy problem and establish the temporal irregularity of the solution.

Article information

Electron. Commun. Probab., Volume 23 (2018), paper no. 36, 12 pp.

Received: 1 June 2017
Accepted: 26 April 2018
First available in Project Euclid: 7 June 2018

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Zentralblatt MATH identifier

Primary: 60H15: Stochastic partial differential equations [See also 35R60] 60G52: Stable processes 60G20: Generalized stochastic processes 47D06: One-parameter semigroups and linear evolution equations [See also 34G10, 34K30]

cylindrical Lèvy processes stochastic partial differential equations stable distributions

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Riedle, Markus. Stable cylindrical Lévy processes and the stochastic Cauchy problem. Electron. Commun. Probab. 23 (2018), paper no. 36, 12 pp. doi:10.1214/18-ECP134. https://projecteuclid.org/euclid.ecp/1528358641

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