Multivariate central limit theorems for averages of fractional Volterra processes and applications to parameter estimation

TL;DR

This paper proves multivariate normal convergence for averages of fractional Volterra processes derived from fractional Brownian motion with Hurst parameter greater than 1/2, and explores applications to parameter estimation.

Contribution

It establishes multivariate CLTs for fractional Volterra processes and applies these results to improve parameter estimation methods.

Findings

Proves multivariate normal convergence for fractional Volterra process averages.

Provides new insights into parameter estimation for processes driven by fractional Brownian motion.

Extends CLT results to a class of non-Markovian processes.

Abstract

The purpose of this paper is to establish the multivariate normal convergence for the average of certain Volterra processes constructed from a fractional Brownian motion with Hurst parameter H>1/2. Some applications to parameter estimation are then discussed.