Level Sets and Extrema of Random Processes and Fields

Beschreibung

A timely and comprehensive treatment of random field theory withapplications across diverse areas of study Level Sets and Extrema of Random Processes and Fields discusseshow to understand the properties of the level sets of paths as wellas how to compute the probability distribution of its extremalvalues, which are two general classes of problems that arise in thestudy of random processes and fields and in related applications.This book provides a unified and accessible approach to these twotopics and their relationship to classical theory and Gaussianprocesses and fields, and the most modern research findings arealso discussed. The authors begin with an introduction to the basic concepts ofstochastic processes, including a modern review of Gaussian fieldsand their classical inequalities. Subsequent chapters are devotedto Rice formulas, regularity properties, and recent results on thetails of the distribution of the maximum. Finally, applications ofrandom fields to various areas of mathematics are provided,specifically to systems of random equations and condition numbersof random matrices. Throughout the book, applications are illustrated from variousareas of study such as statistics, genomics, and oceanography whileother results are relevant to econometrics, engineering, andmathematical physics. The presented material is reinforced byend-of-chapter exercises that range in varying degrees ofdifficulty. Most fundamental topics are addressed in the book, andan extensive, up-to-date bibliography directs readers to existingliterature for further study. Level Sets and Extrema of Random Processes and Fields is anexcellent book for courses on probability theory, spatialstatistics, Gaussian fields, and probabilistic methods in realcomputation at the upper-undergraduate and graduate levels. It isalso a valuable reference for professionals in mathematics andapplied fields such as statistics, engineering, econometrics,mathematical physics, and biology.

Autor*in

Jean-Marc Azais

Themen in »Level Sets and Extrema of Random Processes and Fields«

Probability & Mathematical Statistics Statistics Statistik Wahrscheinlichkeitsrechnung Wahrscheinlichkeitsrechnung u. mathematische Statistik

Stimmen zu »Level Sets and Extrema of Random Processes and Fields«

"It is a very original book, distinguished by its topic and itsability to make use of intuitive basic techniques, such as the Riceformula for instance. So we can say already that it is one of themost important books in probability theory published in the lasttwenty years." (Zentralblatt Math, 2010)
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