Space-time continuous solutions to SPDE's driven by a homogeneous Wiener process

Brzeźniak, Zdzisław ; Peszat, Szymon

Studia Mathematica, Tome 133 (1999), p. 261-299 / Harvested from The Polish Digital Mathematics Library

Résumé

Stochastic partial differential equations on $ℝ^d$ are considered. The noise is supposed to be a spatially homogeneous Wiener process. Using the theory of stochastic integration in Banach spaces we show the existence of a Markovian solution in a certain weighted $L^q$-space. Then we obtain the existence of a space continuous solution by means of the Da Prato, Kwapień and Zabczyk factorization identity for stochastic convolutions.

Détail

Publié le : 1999-01-01

Zbl 0944.60075

EUDML-ID : urn:eudml:doc:216686

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