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Trawl Processes

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Ambit Stochastics

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

Abstract

A particular simple case of ambit fields are the trawl processes, which we study in this chapter. Such (purely temporal) processes are constructed by evaluating a Lévy basis over stationary ambit sets. Trawl processes, although very simplistic, provide an amazingly rich family of stationary stochastic processes in time, where the temporal dependence structure is specified through the ambit sets. An application to high-frequency financial time series data demonstrates the flexibility and attractiveness of trawl processes.

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Notes

  1. 1.

    We say that a random variable follows the standard uniform distribution if it is uniformly distributed on the interval [0,  1].

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Author information

Authors and Affiliations

  1. Department of Mathematics, University of Aarhus, Aarhus, Denmark

    Ole E. Barndorff-Nielsen

  2. Department of Mathematics, University of Oslo, Oslo, Norway

    Fred Espen Benth

  3. Department of Mathematics, Imperial College London, London, UK

    Almut E. D. Veraart

Authors
  1. Ole E. Barndorff-Nielsen
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  2. Fred Espen Benth
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  3. Almut E. D. Veraart
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Barndorff-Nielsen, O.E., Benth, F.E., Veraart, A.E.D. (2018). Trawl Processes. In: Ambit Stochastics. Probability Theory and Stochastic Modelling, vol 88. Springer, Cham. https://doi.org/10.1007/978-3-319-94129-5_8

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