Lévy-based Tempo-Spatial Modelling; with Applications to Turbulence

Ole E. Barndorff-Nielsen and Jürgen Schmiegel


This paper discusses certain types of tempo-spatial models constructed from Lévy bases. The dynamics are described by a field of stochastic processes.

We first consider OU (Ornstein-Uhlenbeck) fields representing several extensions of the concept of OU processes (processes of Ornstein-Uhlenbeck type), with the main focus on the potential for dynamic modelling. Applications to dynamical spatial processes of Cox type are briefly indicated.

The second part of the paper discusses the modelling of tempo-spatial correlations of SI (stochastic intermittency) fields. SI fields can be thought of as a dynamical, continuous and homogeneous generalisation of turbulent cascades. In this respect we construct an SI field with tempo-spatial scaling behaviour that accords with the energy dissipation observed in turbulent flows. Some parallels of this construction are also briefly sketched.