 On the divergence and vorticity of vector ambit fieldsOrimar Sauri Stochastic Processes and their Applications, 2020, vol. 130, issue 10, 6184-6225 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. Keywords: Ambit fields; Divergence; Infinite divisible stationary and isotropic fields; 2-dimensional turbulence; Stokes’ Theorem (search for similar items in EconPapers) Downloads: (external link) Related works: Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text Persistent link: https://EconPapers.repec.org/RePEc:eee:spapps:v:130:y:2020:i:10:p:6184-6225 Ordering information: This journal article can be ordered from DOI: 10.1016/j.spa.2020.05.007 Access Statistics for this article Stochastic Processes and their Applications is currently edited by T. Mikosch More articles in Stochastic Processes and their Applications from Elsevier |
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