Limit theorems for local and occupation times of random walks and Brownian motion on a spider

TL;DR

This paper establishes limit theorems for local and occupation times of simple random walks and Brownian motion on a spider graph with multiple legs, providing strong approximations and asymptotic results.

Contribution

It introduces new limit theorems for local and occupation times of processes on a spider graph, extending classical results to this structured setting.

Findings

Limit theorems for local times on a spider graph

Strong approximation of random walks and Brownian motion

Asymptotic behavior of occupation times for fixed number of legs

Abstract

A simple random walk and a Brownian motion are considered on a spider that is a collection of half lines (we call them legs) joined in the origin. We give a strong approximation of these two objects and their local times. For fixed number of legs we establish limit theorems on local and occupation times in n steps.