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Ambit processes and stochastic partial differential equations

Author

Listed:
  • 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.

Suggested Citation

  • Ole E. Barndorff–Nielsen & Fred Espen Benth & Almut E. D. Veraart, 2010. "Ambit processes and stochastic partial differential equations," CREATES Research Papers 2010-17, Department of Economics and Business Economics, Aarhus University.
    • Handle: RePEc:aah:create:2010-17
    as

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    File URL: https://repec.econ.au.dk/repec/creates/rp/10/rp10_17.pdf
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    References listed on IDEAS

    as
    1. Veraart, Almut E.D., 2010. "Inference For The Jump Part Of Quadratic Variation Of Itô Semimartingales," Econometric Theory, Cambridge University Press, vol. 26(2), pages 331-368, April.
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    Cited by:

    1. Ole E. Barndorff-Nielsen, 2016. "Assessing Gamma kernels and BSS/LSS processes," CREATES Research Papers 2016-09, Department of Economics and Business Economics, Aarhus University.
    2. Fred Espen Benth & Heidar Eyjolfsson, 2016. "Simulation of volatility modulated Volterra processes using hyperbolic stochastic partial differential equations," Papers 1602.02907, arXiv.org.
    3. Fred Espen Benth & Heidar Eyjolfsson, 2015. "Representation and approximation of ambit fields in Hilbert space," Papers 1509.08272, arXiv.org.
    4. Pakkanen, Mikko S., 2014. "Limit theorems for power variations of ambit fields driven by white noise," Stochastic Processes and their Applications, Elsevier, vol. 124(5), pages 1942-1973.
    5. Fred Espen Benth & Paul Kruhner, 2014. "Derivatives pricing in energy markets: an infinite dimensional approach," Papers 1412.7943, arXiv.org.
    6. 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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    More about this item

    Keywords

    Ambit processes; stochastic partial differential equations; Lévy bases; Lévy noise; Walsh theory of martingale measures; turbulence; finance;
    All these keywords.

    JEL classification:

    • C0 - Mathematical and Quantitative Methods - - General
    • C1 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General
    • C5 - Mathematical and Quantitative Methods - - Econometric Modeling

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