Joint H\"older continuity of local time for a class of interacting branching measure valued diffusions

TL;DR

This paper establishes the joint Hölder continuity of local times for certain superprocesses with dependent spatial motion in 2D and 3D, using Tanaka representation and PDE estimates.

Contribution

It introduces a novel approach combining Tanaka representation and PDE estimates to prove Hölder continuity of local times for interacting superprocesses.

Findings

Proved joint Hölder continuity in 2D and 3D.

Developed sharp estimates for local times.

Applied PDE theory to stochastic process analysis.

Abstract

Using a Tanaka representation of the local time for a class of superprocesses with dependent spatial motion, as well as sharp estimates from the theory of uniformly parabolic partial differential equations, the joint H\"older continuity in time and space of said local times is obtained in two and three dimensional Euclidean space.