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Mathematics - Probability Theory and Stochastic Processes | Stochastic analysis for Poisson point processes: Malliavin calculus, Wiener-Itô chaos expansions and stochastic geometry

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

Series: Bocconi & Springer Series, Vol. 7

Peccati, Giovanni, Reitzner, Matthias

2015, Approx. 450 p. 30 illus.

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  • About this book

  • A self-contained introduction to the two important topics of stochastic geometry and infinite-dimensional stochastic analysis
  • First book providing a unified presentation of Malliavin calculus on Poisson spaces from the specific standpoint of limit theorems
  • Composed of in-depth surveys written by undisputed authorities in the domain
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.  

Content Level » Research

Keywords » Limit theorems - Malliavin calculus - Point processes - Stochastic analysis - Stochastic geometry

Related subjects » Applications - Geometry & Topology - Probability Theory and Stochastic Processes

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