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.
Les mer
Part I The purely temporal case.- 1 Volatility modulated Volterra processes.- 2 Simulation.- 3 Asymptotic theory for power variation of LSS processes.- 4 Integration with respect to volatility modulated Volterra processes.- Part II The spatio-temporal case.- 5 The ambit framework.- 6 Representation and simulation of ambit fields.- 7 Stochastic integration with ambit fields as integrators.- 8 Trawl processes.- Part III Applications.- 9 Turbulence modelling.- 10 Stochastic modelling of energy spot prices by LSS processes.- 11 Forward curve modelling by ambit fields.- Appendix A: Bessel functions.- Appendix B: Generalised hyperbolic distribution.- References.- Index.
Les mer
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.
Les mer
“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)
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Written by the leading experts in the field Presents current state of the art Provides theoretical foundations and presents applications in great detail

Produktdetaljer

ISBN
9783319941288
Publisert
2018-11-12
Utgiver
Vendor
Springer International Publishing AG
Høyde
235 mm
Bredde
155 mm
Aldersnivå
Research, P, 06
Språk
Product language
Engelsk
Format
Product format
Innbundet

Biographical note

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.