Stochastic evolution equations driven by cylindrical stable noise

2021/08/03 by Kosmala, Tomasz, Riedle, Markus · 1 citation
#47D06 #60G51 #60G52 #60H15 #FOS: Mathematics #Probability (math.PR)

paper · doi:10.48550/arxiv.2108.01746

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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• Stochastic dissipative systems in Banach spaces driven by Lévy noise

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