FRACTAL GEOMETRY OF LEVY-BASED SPATIAL-TEMPORAL RANDOM FIELDS

摘要

Let X = {X(t, x), t ∈ R, x ∈ Rd} be a Levy-based spatial-temporal random field proposed by Barndorff–Nielsen and Schmiegel1 for dynamic modeling of turbulence. We describe some fractal geometry for this field, with a view toward a proper non-Gaussian aspect of Mandelbrot’s paper.2 Recent progress on multifractal scalings of the stationary exponential processes is also reported, and is toward the intermittency fields proposed in Barndorff-Nielsen and Schmiegel.1