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 …

In his forward-looking paper [374] at the conference “Mathematics Towards the Third
Millennium,” our esteemed colleague at Brown University Prof. David Mumford argued that …

In this paper, we study the Cauchy problem for a quasilinear degenerate parabolic
stochastic partial differential equation driven by a cylindrical Wiener process. In particular …

We study the Cauchy problem for a scalar semilinear degenerate parabolic partial
differential equation with stochastic forcing. In particular, we are concerned with the well …

We study the Cauchy problem for multi-dimensional nonlinear conservation laws with
multiplicative stochastic perturbation. Using the concept of measure-valued solutions and …

We are concerned with multidimensional stochastic balance laws. We identify a class of
nonlinear balance laws for which uniform spatial BV bound for vanishing viscosity …

In this paper we prove the well-posedness of the generalized Dean–Kawasaki equation
driven by noise that is white in time and colored in space. The results treat diffusion …

We develop a pathwise theory for scalar conservation laws with quasilinear multiplicative
rough path dependence, a special case being stochastic conservation laws with quasilinear …

We study the long‐time behavior and regularity of the pathwise entropy solutions to
stochastic scalar conservation laws with random‐in‐time spatially homogeneous fluxes and …

We study quasilinear degenerate parabolic-hyperbolic stochastic partial differential
equations with general multiplicative noise within the framework of kinetic solutions. Our …