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1999 | 137 | 3 | 261-299
Tytuł artykułu

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

Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
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.
Czasopismo
Rocznik
Tom
137
Numer
3
Strony
261-299
Opis fizyczny
Daty
wydano
1999
otrzymano
1998-03-03
poprawiono
1999-01-11
Twórcy
  • Institute of Mathematics, Polish Academy of Sciences, Św. Tomasza 30/7, 31-027 Kraków, Poland, napeszat@cyf-kr.edu.pl
Bibliografia
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  • [9] M. Capiński and S. Peszat, On the existence of a solution to stochastic Navier-Stokes equations, Nonlinear Anal., to appear.
  • [10] G. Da Prato, S. Kwapień and J. Zabczyk, Regularity of solutions of linear stochastic equations in Hilbert spaces, Stochastics 23 (1987), 1-23.
  • [11] G. Da Prato and J. Zabczyk, Stochastic Equations in Infinite Dimensions, Cambridge Univ. Press, Cambridge, 1992.
  • [12] G. Da Prato and J. Zabczyk, Ergodicity for Infinite Dimensional Systems, Cambridge Univ. Press, Cambridge, 1996.
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  • [32] S. Peszat and J. Seidler, Maximal inequalities and space-time regularity of stochastic convolutions, Math. Bohem. 123 (1998), 7-32.
  • [33] S. Peszat and J. Zabczyk, Strong Feller property and irreducibility for diffusions on Hilbert spaces, Ann. Probab. 23 (1995), 157-172.
  • [34] S. Peszat and J. Zabczyk, Stochastic evolution equations with a spatially homogeneous Wiener process, Stochastic Process. Appl. 72 (1997), 187-204.
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  • [38] G. Tessitore and J. Zabczyk, Invariant measures for stochastic heat equations, Probab. Math. Statist. 18 (1999), 271-287.
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Bibliografia
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