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 …

The theory of large deviations is concerned with various approximations involving rare
events. It is also concerned with characterizing the circumstances that lead to a given rare …

As a relatively new area in mathematics, stochastic partial differential equations (PDEs) are
still at a tender age and have not yet received much attention in the mathematical …

We deal with a class of abstract nonlinear stochastic models, which covers many 2D
hydrodynamical models including 2D Navier-Stokes equations, 2D MHD models and the 2D …

We consider a system of diffusion processes that interact through their empirical mean and
have a stabilizing force acting on each of them, corresponding to a bistable potential. There …

A variational formula for positive functionals of a Poisson random measure and Brownian
motion is proved. The formula is based on the relative entropy representation for exponential …

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 …

Stochastic partial differential equations driven by Poisson random measures (PRMs) have
been proposed as models for many different physical systems, where they are viewed as a …

We study large deviation properties of systems of weakly interacting particles modeled by Itô
stochastic differential equations (SDEs). It is known under certain conditions that the …

Since we will never really know why the prices of financial assets move, we should at least
make a faithful model of how they move. This was the motivation of Bachelier in 1900, when …