Stochastic analysis for Poisson point processes: Malliavin calculus, Wiener-Itô chaos expansions and stochastic geometry

This book project concerns the connection between two branches of modern (theoretical and applied) probability - namely stochastic geometry and the Malliavin calculus of variations. Due to the strong connections of stochastic geometry to stereology and spatial statistics, results in this area possess a large number of important applications, e.g. to the mathematical modelling and statistical analysis of telecommunication networks. On the other hand, the Malliavin calculus is a collection of probabilistic techniques based on the properties of infinite-dimensional differential operators, acting on smooth functionals of general point processes and Gaussian fields; applications range from mathematical physics to mathematical finance, concentration inequalities and stochastic differential equations. The aim of this book is to convey in a single volume a rigorous yet lively presentation of the many facets of this rapidly evolving area.