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 …

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 …

This book contains a first systematic study of compressible fluid flows subject to stochastic
forcing. The bulk is the existence of dissipative martingale solutions to the stochastic …

Abstract top Different types of uniqueness (eg pathwise uniqueness, uniqueness in law, joint
uniqueness in law) and existence (eg strong solution, martingale solution) for stochastic …

These notes originated from a series of lectures given at Waseda University in April–May
2021, supported by Top Global University Project of Waseda University. The first author …

In this paper we construct a theory of stochastic integration of processes with values in ℒ (H,
E), where H is a separable Hilbert space and E is a UMD Banach space (ie, a space in …

Stochastic evolution equations are studied in M-type 2 Banach spaces framework. Using
factorization method and Burkholder inequality we prove regularity properties of stochastic …

We establish the local existence of pathwise solutions for the stochastic Euler equations in a
three-dimensional bounded domain with slip boundary conditions and a suitable nonlinear …

We discuss existence, uniqueness, and space–time Hölder regularity for solutions of the
parabolic stochastic evolution equation where A generates an analytic C0-semigroup on a …

In this paper, we study the existence-uniqueness and large deviation estimate for stochastic
Volterra integral equations with singular kernels in 2-smooth Banach spaces. Then we apply …