Tanaka formula and local time for a class of interacting branching measure-valued diffusions

TL;DR

This paper constructs superprocesses with dependent spatial motion in Euclidean spaces, establishes the existence of local times for dimensions up to three, and derives a Tanaka formula for these local times.

Contribution

It introduces a new class of superprocesses with dependent spatial motion and proves the existence of local times and a Tanaka formula for them.

Findings

Local times exist for dimensions d ≤ 3.

Constructed superprocesses with dependent spatial motion.

Derived Tanaka formula for local times.

Abstract

We construct superprocesses with dependent spatial motion (SDSMs) in Euclidean spaces $R^d$ with $d\ge1$ and show that,even when they start at some unbounded initial positive Radon measure such as Lebesgue measure on $R^d$, their local times exist when $d\le3$. A Tanaka formula of the local time is also derived.