Self-similar processes are stochastic processes that are invariant in distribution under
suitable time scaling, and are a subject intensively studied in the last few decades. This …

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 this paper linear stochastic evolution equations driven by infinite-dimensional fractional
Brownian motion are studied. A necessary and sufficient condition for the existence and …

We present the Walsh theory of stochastic integrals with respect to martingale measures,
and various extensions of this theory, alongside of the Da Prato and Zabczyk theory of …

Developed in the 1970s to study the existence and smoothness of density for the probability
laws of random vectors, Malliavin calculus--a stochastic calculus of variation on the Wiener …

We consider nonlinear parabolic SPDEs of the form \partial_tu=\calLu+σ(u)̇w, where ̇w
denotes space-time white noise, σ:R→R is globally Lipschitz continuous, and \calL is the …

Existence of an invariant measure for a stochastic extensible beam equation and for a
stochastic damped wave equation with polynomial nonlinearities is proved. It is shown first …

Consider a parabolic stochastic PDE of the form∂ tu= 1 2 Δ u+ σ (u) η, where u= u (t, x) for
t≥ 0 and x∈ R d, σ: R→ R is Lipschitz continuous and non random, and η is a centered …

The authors study the sample path regularity of the solution of a stochastic wave equation in
spatial dimension $ d= 3$. The driving noise is white in time and with a spatially …

The present volume analyzes mathematical models of time-dependent physical phenomena
on three levels: microscopic, mesoscopic, and macroscopic. We provide a rigorous …