Gibbs-Cox random fields and Burgers turbulence. (English) Zbl 0838.60016

Funaki, T.; Surgailis, D.; Woyczynski, W. A.

Ann. Appl. Probab. 5, No. 2, 461-492 (1995).

The functionals on shot-noise fields with spatial distribution driven by the Gibbs-Cox field are studied. This permits to establish the non-Gaussian scaling limits for the solutions of Burger’s equation with shot-noise type initial data mentioned above. It provides a generalization of previous results in this direction. Connections with other related investigations by mathematicians and physicists and possible applications are discussed.

Reviewer: A.V.Bulinskij (Moskva)

MSC:

60F05	Central limit and other weak theorems
60H15	Stochastic partial differential equations (aspects of stochastic analysis)
76F20	Dynamical systems approach to turbulence

Keywords:

Burgers turbulence; shot-noise fields; Gibbs-Cox field; Burger’s equation