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 …

To improve the efficiency of Monte Carlo estimation, practitioners are turning to biased
Markov chain Monte Carlo procedures that trade off asymptotic exactness for computational …

Random Fields on the Sphere presents a comprehensive analysis of isotropic spherical
random fields. The main emphasis is on tools from harmonic analysis, beginning with the …

As is well-known, the classical Brownian motion is a stochastic process which is selfsimilar
of index 1/2 and has stationary increments. It is actually the only continuous Gaussian …

The concept of Wiener chaos generalizes to an infinite-dimensional setting the properties of
orthogonal polynomials associated with probability distributions on the real line. It plays a …

This book provides the reader with the principal concepts and results related to differential
properties of measures on infinite dimensional spaces. In the finite dimensional case such …

There are textbooks and there are research monographs. Some believe that a research
monograph is supposed to bore rather than batter. The following quotation is attributed to …

Stein's method for measuring convergence to a continuous target distribution relies on an
operator characterizing the target and Stein factor bounds on the solutions of an associated …

We combine Stein's method with a version of Malliavin calculus on the Poisson space. As a
result, we obtain explicit Berry–Esséen bounds in Central limit theorems (CLTs) involving …

We establish existence of Stein kernels for probability measures on R^d satisfying a
Poincaré inequality, and obtain bounds on the Stein discrepancy of such measures …