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

In this paper parabolic random partial differential equations and parabolic stochastic partial differential equations driven by a Wiener process are considered. A deterministic, tensorized evolution equation for the second moment and the covariance of the solutions of the parabolic stochastic partial differential equations is derived. Well-posedness of a space-time weak variational formulation ...