Limit theorems for multifractal products of random fields

Abstract: The talk is about random functions with changing local regularity exponent (multifractal processes and multifractal fields in multidimensional cases). This type of random function has been observed in various areas including communication systems, precipitation fields, econometrics, and so on. The goal of this talk is to present new results in the modeling of multifractal random functions. One of the possible approaches to obtain multifractal random functions is as limits of multifractal products of random functions (roughly speaking, integrals of infinite products of random functions). In the talk, I will show new results on the existence of those limits in the spaces Lq as well as new results on the rate of convergence. The developed methodology is also applied to multidimensional multifractal measures. Finally, I will show a new class of examples of geometric φ-sub-Gaussian random functions when the general assumptions have a simple form and can be expressed in terms of covariance functions only.

MathematicsPhysics

Audience: researchers in the topic

Nečas Seminar on Continuum Mechanics

Series comments: This seminar was founded on December 14, 1966.

Faculty of Mathematics and Physics, Charles University, Sokolovská 83, Prague 8. If not written otherwise, we will meet on Mondays at 15:40 in lecture hall K3 (2nd floor)