H"older index at a given point for density states of super-alpha-stable motion of index 1+beta

TL;DR

This paper determines the Hölder regularity index at specific points for density states of super-alpha-stable motions, revealing it exceeds the optimal local Hölder continuity index, thus providing new insights into their regularity properties.

Contribution

It introduces a method to precisely compute the Hölder index at points for density states of super-alpha-stable processes with alpha > 1+beta, showing it surpasses the optimal local index.

Findings

Hölder index at points exceeds the optimal local index.

The regularity of density states is better than previously understood.

Provides a new approach to analyze regularity of superprocess densities.

Abstract

A H"older regularity index at given points for density states of (alpha,1,beta)-superprocesses with alpha>1+beta is determined. It is shown that this index is strictly greater than the optimal index of local H"older continuity for those density states.