From intersection local time to the Rosenblatt process

TL;DR

This paper introduces a particle-based perspective on the Rosenblatt process using intersection local time and white noise analysis, providing insights into its long-range dependence characteristics.

Contribution

It presents a novel particle picture approach to the Rosenblatt process and discusses a new measure called the dependence exponent for long-range dependence.

Findings

Particle picture approach to Rosenblatt process

Introduction of dependence exponent for long-range dependence

Analysis using intersection local time and white noise

Abstract

The Rosenblatt process was obtained by Taqqu (1975) from convergence in distribution of partial sums of strongly dependent random variables. In this paper we give a particle picture approach to the Rosenblatt process with the help of intersection local time and white noise analysis, and discuss measuring its long range dependence by means of a number called dependence exponent.