Multifractal analysis of superprocesses with stable branching in dimension one

TL;DR

This paper demonstrates that the density functions of certain superprocesses exhibit multifractal behavior and computes their spectrum of singularities, advancing understanding of their complex structure.

Contribution

It introduces a multifractal analysis of $(eta,1,eta)$-superprocesses in one dimension, providing explicit spectrum calculations for the first time.

Findings

Density functions are almost surely multifractal.

Spectrum of singularities is explicitly calculated.

Results apply to superprocesses with specific stability parameters.

Abstract

We show that density functions of a $(\alpha,1,\beta)$-superprocesses are almost sure multifractal for $\alpha>\beta+1$, $\beta\in(0,1)$ and calculate the corresponding spectrum of singularities.