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arXiv · 2108.01746

Stochastic evolution equations driven by cylindrical stable noise

Tomasz Kosmala·Markus Riedle
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Abstract

We prove existence and uniqueness of a mild solution of a stochastic evolution equation driven by a standard $\alpha$-stable cylindrical L\'evy process defined on a Hilbert space for $\alpha \in (1,2)$. 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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Tomasz Kosmala, Markus Riedle. 2021-08-03. Stochastic evolution equations driven by cylindrical stable noise. https://arxiv.org/abs/2108.01746

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