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 …

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 consider stochastic differential equations (SDEs) driven by a fractional Brownian motion
with a drift coefficient that is allowed to be arbitrarily close to criticality in a scaling sense. We …

This article is a review of Lévy processes, stochastic integration and existence results for
stochastic differential equations and stochastic partial differential equations driven by Lévy …

We consider the 2D Euler equations on $\mathbb {R}^ 2$ in vorticity form, with unbounded
initial vorticity, perturbed by a suitable non-smooth Kraichnan transport noise. We show …

The theory of the stochastic Navier–Stokes equations (SNSE) has known a lot of important
advances those last 20 years. Existence and uniqueness have been studied in various …

We consider a nonlinear stochastic partial differential equation (SPDE) that takes the form of
the Camassa–Holm equation perturbed by a convective, position-dependent, noise term …

In this paper we investigate a non-linear and non-local one dimensional transport equation
under random perturbations on the real line. We first establish a local-in-time theory, ie …

The primitive equations (PEs) are a basic model in the study of large scale oceanic and
atmospheric dynamics. These systems form the analytical core of the most advanced …

In this paper, we consider the noise effects on a class of stochastic evolution equations
including the stochastic Camassa–Holm equations with or without rotation. We first obtain …