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1999 | 137 | 3 | 261-299
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Space-time continuous solutions to SPDE's driven by a homogeneous Wiener process

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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.
Opis fizyczny
  • Department of Pure Mathematics, The University of Hull, Hull HU6 7RX, United Kingdom
  • Institute of Mathematics, Polish Academy of Sciences, Św. Tomasza 30/7, 31-027 Kraków, Poland
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