Regularity and irregularity of superprocesses with $(1+\beta)$-stable branching mechanism
Probability
2015-08-11 v1
Abstract
We would like to give an overview of results on regularity, or better to say "irregularity", properties of densities at fixed times of super-Brownian motion with -stable branching for . First, the following dichotomy for the density is shown: it is continuous in the dimension and locally unbounded in all higher dimensions where it exists. Then in we determine pointwise and local H\"older exponents of the density, and calculate the multifractal spectrum corresponding to pointwise H\"older exponents.
Keywords
Cite
@article{arxiv.1508.02081,
title = {Regularity and irregularity of superprocesses with $(1+\beta)$-stable branching mechanism},
author = {Leonid Mytnik and Vitali Wachtel},
journal= {arXiv preprint arXiv:1508.02081},
year = {2015}
}