Space-time continuous solutions to SPDE's driven by a homogeneous Wiener process
Zdzisław Brzeźniak; Szymon Peszat
Studia Mathematica (1999)
- Volume: 137, Issue: 3, page 261-299
- ISSN: 0039-3223
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topBrzeźniak, Zdzisław, and Peszat, Szymon. "Space-time continuous solutions to SPDE's driven by a homogeneous Wiener process." Studia Mathematica 137.3 (1999): 261-299. <http://eudml.org/doc/216686>.
@article{Brzeźniak1999,
abstract = {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.},
author = {Brzeźniak, Zdzisław, Peszat, Szymon},
journal = {Studia Mathematica},
keywords = {stochastic partial differential equations in $L^q$-spaces; homogeneous Wiener process; random environment; stochastic integration in Banach spaces; stochastic partial differential equations; continuous solutions},
language = {eng},
number = {3},
pages = {261-299},
title = {Space-time continuous solutions to SPDE's driven by a homogeneous Wiener process},
url = {http://eudml.org/doc/216686},
volume = {137},
year = {1999},
}
TY - JOUR
AU - Brzeźniak, Zdzisław
AU - Peszat, Szymon
TI - Space-time continuous solutions to SPDE's driven by a homogeneous Wiener process
JO - Studia Mathematica
PY - 1999
VL - 137
IS - 3
SP - 261
EP - 299
AB - 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.
LA - eng
KW - stochastic partial differential equations in $L^q$-spaces; homogeneous Wiener process; random environment; stochastic integration in Banach spaces; stochastic partial differential equations; continuous solutions
UR - http://eudml.org/doc/216686
ER -
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Citations in EuDML Documents
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