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Stochastic evolution equations driven by cylindrical stable noise

Research output: Contribution to journalArticlepeer-review

Original languageEnglish
Number of pages37
JournalStochastic Processes and Their Applications
Accepted/In press26 Oct 2021

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  • stable-noise-revised

    stable_noise_revised.pdf, 488 KB, application/pdf

    Uploaded date:02 Nov 2021

    Version:Accepted author manuscript

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Abstract

We prove existence and uniqueness of a mild solution of a stochastic evolution equation driven by a standard α-stable cylindrical Lévy process defined on a Hilbert space for α ∈ (1,2). The coefficients are assumed to map between certain domains of fractional powers of the generator present in the equation. The solution is constructed as a weak limit of the Picard iteration using tightness arguments. Existence of strong solution is obtained by a general version of the Yamada--Watanabe theorem.

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