Regularity and irregularity of superprocesses with (1+β)-stable branching mechanism

2015/08/09 by Leonid Mytnik, Mytnik, Leonid, Vitali Wachtel +1
Mathematics · #28A80 #FOS: Mathematics #Primary 60J80 #Probability (math.PR) #Secondary 60G57 #math.PR #msc:28A80 #msc:60G57 #msc:60J80

paper · pdf · doi:10.48550/arxiv.1508.02081

arxiv created 2015/08/09 · arxiv updated 2015/08/11

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)-stable branching for β<1. First, the following dichotomy for the density is shown: it is continuous in the dimension d=1 and locally unbounded in all higher dimensions where it exists. Then in d=1 we determine pointwise and local Hölder exponents of the density, and calculate the multifractal spectrum corresponding to pointwise Hölder exponents.

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