IDEAS home Printed from https://ideas.repec.org/a/eee/spapps/v130y2020i10p6184-6225.html
   My bibliography  Save this article

On the divergence and vorticity of vector ambit fields

Author

Listed:
  • Sauri, Orimar

Abstract

This paper studies the asymptotic behaviour of the flux and circulation of a subclass of random fields within the family of 2-dimensional vector ambit fields. We show that, under proper normalization, the flux and the circulation converge stably in distribution to certain stationary random fields that are defined as line integrals of a Lévy basis. A full description of the rates of convergence and the limiting fields is given in terms of the roughness of the background driving Lévy basis and the geometry of the ambit set involved. We further discuss the connection of our results with the classical Divergence and Vorticity Theorems. Finally, we introduce a class of models that are capable to reflect stationarity, isotropy and null divergence as key properties.

Suggested Citation

  • Sauri, Orimar, 2020. "On the divergence and vorticity of vector ambit fields," Stochastic Processes and their Applications, Elsevier, vol. 130(10), pages 6184-6225.
    • Handle: RePEc:eee:spapps:v:130:y:2020:i:10:p:6184-6225
    DOI: 10.1016/j.spa.2020.05.007
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0304414918301625
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.spa.2020.05.007?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Jan Rataj & Luděk Zajíček, 2017. "On the structure of sets with positive reach," Mathematische Nachrichten, Wiley Blackwell, vol. 290(11-12), pages 1806-1829, August.
    2. Corcuera, José Manuel & Hedevang, Emil & Pakkanen, Mikko S. & Podolskij, Mark, 2013. "Asymptotic theory for Brownian semi-stationary processes with application to turbulence," Stochastic Processes and their Applications, Elsevier, vol. 123(7), pages 2552-2574.
    3. Braverman, Michael & Samorodnitsky, Gennady, 1998. "Symmetric infinitely divisible processes with sample paths in Orlicz spaces and absolute continuity of infinitely divisible processes," Stochastic Processes and their Applications, Elsevier, vol. 78(1), pages 1-26, October.
    4. Basse, Andreas & Pedersen, Jan, 2009. "Lévy driven moving averages and semimartingales," Stochastic Processes and their Applications, Elsevier, vol. 119(9), pages 2970-2991, September.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    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. Kerstin Gärtner & Mark Podolskij, 2014. "On non-standard limits of Brownian semi-stationary," CREATES Research Papers 2014-50, Department of Economics and Business Economics, Aarhus University.
    3. Ole E. Barndorff-Nielsen & Mikko S. Pakkanen & Jürgen Schmiegel, 2013. "Assessing Relative Volatility/Intermittency/Energy Dissipation," CREATES Research Papers 2013-15, Department of Economics and Business Economics, Aarhus University.
    4. Mikko S. Pakkanen & Anthony Réveillac, 2014. "Functional limit theorems for generalized variations of the fractional Brownian sheet," CREATES Research Papers 2014-14, Department of Economics and Business Economics, Aarhus University.
    5. Sauri, Orimar & Veraart, Almut E.D., 2017. "On the class of distributions of subordinated Lévy processes and bases," Stochastic Processes and their Applications, Elsevier, vol. 127(2), pages 475-496.
    6. Harms, Philipp & Stefanovits, David, 2019. "Affine representations of fractional processes with applications in mathematical finance," Stochastic Processes and their Applications, Elsevier, vol. 129(4), pages 1185-1228.
    7. Bennedsen, Mikkel, 2017. "A rough multi-factor model of electricity spot prices," Energy Economics, Elsevier, vol. 63(C), pages 301-313.
    8. Basse, Andreas & Pedersen, Jan, 2009. "Lévy driven moving averages and semimartingales," Stochastic Processes and their Applications, Elsevier, vol. 119(9), pages 2970-2991, September.
    9. Bender, Christian & Knobloch, Robert & Oberacker, Philip, 2015. "A generalised Itō formula for Lévy-driven Volterra processes," Stochastic Processes and their Applications, Elsevier, vol. 125(8), pages 2989-3022.
    10. Mark Podolskij, 2014. "Ambit fields: survey and new challenges," CREATES Research Papers 2014-51, Department of Economics and Business Economics, Aarhus University.
    11. 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.
    12. Basse-O’Connor, Andreas & Nielsen, Mikkel Slot & Pedersen, Jan, 2018. "Equivalent martingale measures for Lévy-driven moving averages and related processes," Stochastic Processes and their Applications, Elsevier, vol. 128(8), pages 2538-2556.
    13. Mikkel Bennedsen & Ulrich Hounyo & Asger Lunde & Mikko S. Pakkanen, 2016. "The Local Fractional Bootstrap," CREATES Research Papers 2016-15, Department of Economics and Business Economics, Aarhus University.
    14. Benth, Fred Espen & Schroers, Dennis & Veraart, Almut E.D., 2022. "A weak law of large numbers for realised covariation in a Hilbert space setting," Stochastic Processes and their Applications, Elsevier, vol. 145(C), pages 241-268.
    15. Mark Podolskij & Nopporn Thamrongrat, 2015. "A weak limit theorem for numerical approximation of Brownian semi-stationary processes," CREATES Research Papers 2015-53, Department of Economics and Business Economics, Aarhus University.
    16. Barndorff-Nielsen, Ole E. & Benth, Fred Espen & Pedersen, Jan & Veraart, Almut E.D., 2014. "On stochastic integration for volatility modulated Lévy-driven Volterra processes," Stochastic Processes and their Applications, Elsevier, vol. 124(1), pages 812-847.
    17. Andreas Basse, 2009. "Spectral Representation of Gaussian Semimartingales," Journal of Theoretical Probability, Springer, vol. 22(4), pages 811-826, December.
    18. Christian Bender & Alexander Lindner & Markus Schicks, 2012. "Finite Variation of Fractional Lévy Processes," Journal of Theoretical Probability, Springer, vol. 25(2), pages 594-612, June.
    19. Li, Yuan & Pakkanen, Mikko S. & Veraart, Almut E.D., 2023. "Limit theorems for the realised semicovariances of multivariate Brownian semistationary processes," Stochastic Processes and their Applications, Elsevier, vol. 155(C), pages 202-231.
    20. Mikkel Bennedsen & Asger Lunde & Mikko S. Pakkanen, 2014. "Discretization of Lévy semistationary processes with application to estimation," CREATES Research Papers 2014-21, Department of Economics and Business Economics, Aarhus University.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:spapps:v:130:y:2020:i:10:p:6184-6225. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/wps/find/journaldescription.cws_home/505572/description#description .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.