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ArticleOriginal scientific text

Title

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

Authors 1, 2

Affiliations

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

Abstract

Stochastic partial differential equations on ℝd 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 Lq-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.

Keywords

ENG
stochastic partial differential equations in Lq-spaces, homogeneous Wiener process, random environment, stochastic integration in Banach spaces

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Studia Mathematica
1999/137/3
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Pages:
261-299
Main language of publication
English
Received
1998-03-03
Accepted
1999-01-11
Published
1999
Exact and natural sciences