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Space-time fractional stochastic equations on regular bounded open domains. (English) Zbl 1354.60065

Summary: Fractional (in time and in space) evolution equations defined on Dirichlet regular bounded open domains, driven by fractional integrated in time Gaussian spatiotemporal white noise, are considered here. Sufficient conditions for the definition of a weak-sense Gaussian solution, in the mean-square sense, are derived. The temporal, spatial and spatiotemporal Hölder continuity, in the mean-square sense, of the formulated solution is obtained, under suitable conditions, from the asymptotic properties of the Mittag-Leffler function, and the asymptotic order of the eigenvalues of a fractional polynomial of the Dirichlet negative Laplacian operator on such bounded open domains.

MSC:

60H15 Stochastic partial differential equations (aspects of stochastic analysis)
60G22 Fractional processes, including fractional Brownian motion
60G60 Random fields
60G15 Gaussian processes
60G20 Generalized stochastic processes
60G17 Sample path properties
60G12 General second-order stochastic processes
26A33 Fractional derivatives and integrals
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