Ambit Stochastics

By: Almut E. D. Veraart, Ole E. Barndorff-Nielsen, Fred Espen Benth

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Hardcover | 12 November 2018

At a Glance

Hardcover
430 Pages

Dimensions(cm)
16.2 x 24.1 x 3.1

Hardcover

$199.00

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Drawing on advanced probability theory, Ambit Stochastics is used to model stochastic processes which depend on both time and space. This monograph, the first on the subject, provides a reference for this burgeoning field, complete with the applications that have driven its development.

Unique to Ambit Stochastics are ambit sets, which allow the delimitation of space-time to a zone of interest, and ambit fields, which are particularly well-adapted to modelling stochastic volatility or intermittency. These attributes lend themselves notably to applications in the statistical theory of turbulence and financial econometrics. In addition to the theory and applications of Ambit Stochastics, the book also contains new theory on the simulation of ambit fields and a comprehensive stochastic integration theory for Volterra processes in a non-semimartingale context.

Written by pioneers in the subject, this book will appeal to researchers and graduate students interested in empirical stochastic modelling.

Industry Reviews

"The author pays a great attention to diverse methods of numerical integration and simulation algorithms. ... The authors have written a fundamental book on contemporary probability theory and its applications. The book can be strongly recommended to theorists and applied scientists." (Jordan M. Stoyanov, zbMATH 1472.60002, 2021)"

"The book is very well written ... . this monograph is particularly suitable for getting acquainted with the subject, or for getting precise material on one particular sub-topic about ambit fields." (Anthony R©veillac, Mathematical Reviews, January, 2020)

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