English

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 (1+β)(1+\beta)-stable branching for β<1\beta<1. First, the following dichotomy for the density is shown: it is continuous in the dimension d=1d=1 and locally unbounded in all higher dimensions where it exists. Then in d=1d=1 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}
}