On the divergence and vorticity of vector ambit fields

Orimar Sauri*

*Corresponding author for this work

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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.

Original languageEnglish
JournalStochastic Processes and Their Applications
Pages (from-to)6184-6225
Number of pages42
Publication statusPublished - Oct 2020


  • 2-dimensional turbulence
  • Ambit fields
  • Divergence
  • Infinite divisible stationary and isotropic fields
  • Stokes’ Theorem


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