Geodesic
Space-time continuous solutions to SPDE's driven by a homogeneous Wiener process
Studia Mathematica, Tome 137 (1999) no. 3, pp. 261-299

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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.
DOI : 10.4064/sm-137-3-261-299
Keywords: stochastic partial differential equations in $L^q$-spaces, homogeneous Wiener process, random environment, stochastic integration in Banach spaces

Zdzisław Brzeźniak 1 ; Szymon Peszat 1

1 
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Zdzisław Brzeźniak; Szymon Peszat. Space-time continuous solutions to SPDE's driven by a homogeneous Wiener process. Studia Mathematica, Tome 137 (1999) no. 3, pp. 261-299. doi: 10.4064/sm-137-3-261-299

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