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

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Brzeźniak Z., Peszat S.

Studia Mathematica

1999

tom 137

nr 3

261-299

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.

Ograniczanie wyników

1 Studia Mathematica

1 Brzeźniak Z.

1 Peszat S.

1 1999

Wyniki wyszukiwania

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