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Ambit Stochastics

  • Ole E. Barndorff-Nielsen
  • Fred Espen Benth
  • Almut E. D. Veraart

Part of the Probability Theory and Stochastic Modelling book series (PTSM, volume 88)

Table of contents

  1. Front Matter
    Pages i-xxv
  2. The Purely Temporal Case

    1. Front Matter
      Pages 1-1
    2. Ole E. Barndorff-Nielsen, Fred Espen Benth, Almut E. D. Veraart
      Pages 3-47
    3. Ole E. Barndorff-Nielsen, Fred Espen Benth, Almut E. D. Veraart
      Pages 49-98
    4. Ole E. Barndorff-Nielsen, Fred Espen Benth, Almut E. D. Veraart
      Pages 99-114
    5. Ole E. Barndorff-Nielsen, Fred Espen Benth, Almut E. D. Veraart
      Pages 115-149
  3. The Spatio-Temporal Case

    1. Front Matter
      Pages 151-151
    2. Ole E. Barndorff-Nielsen, Fred Espen Benth, Almut E. D. Veraart
      Pages 153-202
    3. Ole E. Barndorff-Nielsen, Fred Espen Benth, Almut E. D. Veraart
      Pages 203-230
    4. Ole E. Barndorff-Nielsen, Fred Espen Benth, Almut E. D. Veraart
      Pages 231-271
    5. Ole E. Barndorff-Nielsen, Fred Espen Benth, Almut E. D. Veraart
      Pages 273-300
  4. Applications

    1. Front Matter
      Pages 301-301
    2. Ole E. Barndorff-Nielsen, Fred Espen Benth, Almut E. D. Veraart
      Pages 303-332
    3. Ole E. Barndorff-Nielsen, Fred Espen Benth, Almut E. D. Veraart
      Pages 333-351
    4. Ole E. Barndorff-Nielsen, Fred Espen Benth, Almut E. D. Veraart
      Pages 353-376
  5. Back Matter
    Pages 377-402

About this book

Introduction

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.

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

Authors and affiliations

  • Ole E. Barndorff-Nielsen
    • 1
  • Fred Espen Benth
    • 2
  • Almut E. D. Veraart
    • 3
  1. 1.Department of MathematicsUniversity of AarhusAarhusDenmark
  2. 2.Department of MathematicsUniversity of OsloOsloNorway
  3. 3.Department of MathematicsImperial College LondonLondonUK

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-319-94129-5
  • Copyright Information Springer Nature Switzerland AG 2018
  • Publisher Name Springer, Cham
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-3-319-94128-8
  • Online ISBN 978-3-319-94129-5
  • Series Print ISSN 2199-3130
  • Series Online ISSN 2199-3149
  • Buy this book on publisher's site