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Ambit processes and stochastic partial differential equations

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Author Info

  • Ole E. Barndorff–Nielsen

    ()
    (Thiele Center, Department of Mathematical Sciences and CREATES)

  • Fred Espen Benth

    ()
    (Centre of Mathematics for Applications, University of Oslo and Faculty of Economics University of Agder)

  • Almut E. D. Veraart

    ()
    (CREATES, School of Economics and Management Aarhus University)

Abstract

Ambit processes are general stochastic processes based on stochastic integrals with respect to Lévy bases. Due to their flexible structure, they have great potential for providing realistic models for various applications such as in turbulence and finance. This papers studies the connection between ambit processes and solutions to stochastic partial differential equations. We investigate this relationship from two angles: from the Walsh theory of martingale measures and from the viewpoint of the Lévy noise analysis.

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File URL: ftp://ftp.econ.au.dk/creates/rp/10/rp10_17.pdf
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Bibliographic Info

Paper provided by School of Economics and Management, University of Aarhus in its series CREATES Research Papers with number 2010-17.

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Length: 35
Date of creation: 27 Apr 2010
Date of revision:
Handle: RePEc:aah:create:2010-17

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Web page: http://www.econ.au.dk/afn/

Related research

Keywords: Ambit processes; stochastic partial differential equations; Lévy bases; Lévy noise; Walsh theory of martingale measures; turbulence; finance;

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References

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  1. Veraart, Almut E.D., 2010. "Inference For The Jump Part Of Quadratic Variation Of Itô Semimartingales," Econometric Theory, Cambridge University Press, vol. 26(02), pages 331-368, April.
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Cited by:
  1. Ole E. Barndorff-Nielsen & Fred Espen Benth & Almut E. D. Veraart, 2013. "Modelling energy spot prices by volatility modulated L\'{e}vy-driven Volterra processes," Papers 1307.6332, arXiv.org.

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