This book provides an introduction to the theory of stochastic partial differential equations
(SPDEs) of evolutionary type. SPDEs are one of the main research directions in probability …

The paper is concerned with the problem of regularization by noise of 3D Navier–Stokes
equations. As opposed to several attempts made with additive noise which remained …

We investigate well-posedness for martingale solutions of stochastic differential equations,
under low regularity assumptions on their coefficients, widely extending the results first …

A stochastic linear transport equation with multiplicative noise is considered and the
question of no-blow-up is investigated. The drift is assumed only integrable to a certain …

In this paper, we consider McKean-Vlasov stochastic differential equations (MVSDEs) driven
by Lévy noise. By identifying the right equations satisfied by the solutions of the MVSDEs …

In this paper, we establish the existence of a stochastic flow of Sobolev diffeomorphisms
R^d∋x\quad⟼\quads,t(x)∈R^d,\qquads,t∈R for a stochastic differential equation (SDE) of …

We study a stochastic Landau–Lifshitz equation on a bounded interval and with finite
dimensional noise. We first show that there exists a pathwise unique solution to this …

We develop a martingale approach for a class of singular stochastic PDEs of Burgers type
(including fractional and multi-component Burgers equations) by constructing a domain for …

Stochastic Navier-Stokes Equations and Related Models Page 1 Stochastic Navier-Stokes
Equations and Related Models Luigi Amedeo Bianchi and Franco Flandoli In honour of …

A fully discrete approximation of the one-dimensional stochastic heat equation driven by
multiplicative space–time white noise is presented. The standard finite difference …