Overview
- Written by the leading experts in the field
- Presents current state of the art
- Provides theoretical foundations and presents applications in great detail
Part of the book series: Probability Theory and Stochastic Modelling (PTSM, volume 88)
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Table of contents (11 chapters)
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Front Matter
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The Spatio-Temporal Case
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Front Matter
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Back Matter
Keywords
- 60G60, 60F05, 60H05, 60H07, 60H15, 60H20, 60J75, 62F12
- 62H11, 62M10, 62M30, 62P20, 62P35, 65C30, 76F55, 76M35
- 91B25, 91B70
- Volterra processes
- Lévy processes
- Ambit fields
- volatility/intermittency
- statistical turbulence
- power variation
- stochastic partial differential equations
- stochastic PDEs
- random fields
- Lévy basis
- energy markets
- stochastic integration
- non-semimartingales
- Trawl processes
- quantitative finance
About this book
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.
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 Réveillac, Mathematical Reviews, January, 2020)
Authors and Affiliations
About the authors
Ole Barndorff-Nielsen is well known for his manifold contributions to the theory and applications of probability and mathematical statistics, as described in the introductions of The Fascination of Probability, Statistics and Their Applications, Springer 2016. He has contributed to various fields, including statistical inference, sedimentology, infinite divisibility and Levy theory, homogeneous turbulence, and financial econometrics. Together with Jürgen Schmiegel he has founded the field of ambit stochastics.
Fred Espen Benth’s research focuses on stochastic analysis and its applications to energy and finance. He has contributed to risk management analysis of financial markets for weather and energy, as well as theoretical developments of stochastic calculus, including non-semimartingale stochastic integration. Recently he has developed stochastic volatility models and autoregressive processes in the infinite dimensional context.
Almut E. D. Veraart is a statistician and probabilist with an interest in developing stochastic models and statistical methods for finance, energy markets and weather and environmental variables. Her main methodological contributions are in statistical finance focusing on stochastic volatility modelling and estimation based on high-frequency data and in spatio-temporal statistics dealing with simulation and inference for ambit fields.
Bibliographic Information
Book Title: Ambit Stochastics
Authors: Ole E. Barndorff-Nielsen, Fred Espen Benth, Almut E. D. Veraart
Series Title: Probability Theory and Stochastic Modelling
DOI: https://doi.org/10.1007/978-3-319-94129-5
Publisher: Springer Cham
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: Springer Nature Switzerland AG 2018
Hardcover ISBN: 978-3-319-94128-8Published: 12 November 2018
Softcover ISBN: 978-3-030-06802-8Published: 20 December 2018
eBook ISBN: 978-3-319-94129-5Published: 01 November 2018
Series ISSN: 2199-3130
Series E-ISSN: 2199-3149
Edition Number: 1
Number of Pages: XXV, 402
Number of Illustrations: 14 b/w illustrations, 25 illustrations in colour
Topics: Probability Theory and Stochastic Processes, Mathematical Applications in the Physical Sciences, Quantitative Finance, Mathematical Physics, Statistics for Business, Management, Economics, Finance, Insurance, Statistics for Engineering, Physics, Computer Science, Chemistry and Earth Sciences