TY - JOUR
T1 - On the divergence and vorticity of vector ambit fields
AU - Sauri, Orimar
PY - 2020/10
Y1 - 2020/10
N2 - 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.
AB - 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.
KW - 2-dimensional turbulence
KW - Ambit fields
KW - Divergence
KW - Infinite divisible stationary and isotropic fields
KW - Stokes’ Theorem
UR - http://www.scopus.com/inward/record.url?scp=85086368324&partnerID=8YFLogxK
U2 - 10.1016/j.spa.2020.05.007
DO - 10.1016/j.spa.2020.05.007
M3 - Journal article
AN - SCOPUS:85086368324
SN - 0304-4149
VL - 130
SP - 6184
EP - 6225
JO - Stochastic Processes and Their Applications
JF - Stochastic Processes and Their Applications
IS - 10
ER -