[图书][B] Analysis in Banach spaces

Over the past fifteen years, motivated by regularity problems in evolution equations, there
has been tremendous progress in the analysis of Banach space-valued functions and …

[图书][B] Stochastic equations in infinite dimensions

G Da Prato, J Zabczyk - 2014 - books.google.com
Now in its second edition, this book gives a systematic and self-contained presentation of
basic results on stochastic evolution equations in infinite dimensional, typically Hilbert and …

Asymptotic compactness and absorbing sets for 2D stochastic Navier-Stokes equations on some unbounded domains

Z Brzeźniak, Y Li - Transactions of the American Mathematical Society, 2006 - ams.org
We introduce a notion of an asymptotically compact (AC) random dynamical system (RDS).
We prove that for an AC RDS the $\Omega $-limit set $\Omega _B (\omega) $ of any …

Phase reduction of waves, patterns, and oscillations subject to spatially extended noise

J MacLaurin - SIAM Journal on Applied Mathematics, 2023 - SIAM
In this paper we present a framework in which one can rigorously study the effect of spatio-
temporal noise on traveling waves, stationary patterns, and oscillations that are invariant …

Well-posedness of the 3D stochastic primitive equations with multiplicative and transport noise

Z Brzeźniak, J Slavik - Journal of Differential Equations, 2021 - Elsevier
We show that the stochastic 3D primitive equations with the Neumann boundary condition
on the top, the lateral Dirichlet boundary condition and either the Dirichlet or the Neumann …

Maximal inequalities and exponential estimates for stochastic convolutions driven by Lévy-type processes in Banach spaces with application to stochastic quasi …

J Zhu, Z Brzeźniak, W Liu - SIAM Journal on Mathematical Analysis, 2019 - SIAM
We present remarkably simple proofs of Burkholder--Davis--Gundy inequalities for
stochastic integrals and maximal inequalities for stochastic convolutions in Banach spaces …

A note on maximal inequality for stochastic convolutions

E Hausenblas, J Seidler - Czechoslovak Mathematical Journal, 2001 - dml.cz
Czechoslovak Mathematical Journal Page 1 Czechoslovak Mathematical Journal Erika
Hausenblas; Jan Seidler A note on maximal inequality for stochastic convolutions …

Reflection of stochastic evolution equations in infinite dimensional domains

Z Brzeźniak, T Zhang - Annales de l'Institut Henri Poincare (B) …, 2023 - projecteuclid.org
Reflection of stochastic evolution equations in infinite dimensional domains Page 1 Annales de
l’Institut Henri Poincaré - Probabilités et Statistiques 2023, Vol. 59, No. 3, 1549–1571 …

Maximal inequalities for stochastic convolutions in 2-smooth Banach spaces and applications to stochastic evolution equations

J van Neerven, M Veraar - Philosophical Transactions of …, 2020 - royalsocietypublishing.org
Maximal inequalities for stochastic convolutions in 2-smooth Banach spaces and applications to
stochastic evolution equations | Philosophical Transactions of the Royal Society A …

Analysis in Banach spaces

T Hytönen, J van Neerven, M Veraar, L Weis - Volume II: Probabilistic …, 2017 - Springer
Originally conceived to be the final volume of a trilogy on Analysis in Banach spaces,
containing the applications of the infrastructure of Volumes I–II to Harmonic and Stochastic …