Optimal rates for parameter estimation of stationary Gaussian processes

TL;DR

This paper investigates the convergence rates in central limit theorems for functionals of stationary and non-stationary Gaussian sequences, with applications to estimating drift parameters in SDEs driven by fractional Brownian motion.

Contribution

It introduces optimal analysis techniques on Wiener space to determine convergence rates and applies these results to parameter estimation in fractional Brownian motion-driven SDEs.

Findings

Established optimal convergence rates for Gaussian process functionals.

Applied results to drift parameter estimation in fractional Brownian motion SDEs.

Provided new tools for analyzing non-stationary Gaussian sequences.

Abstract

We study rates of convergence in central limit theorems for partial sum of functionals of general stationary and non-stationary Gaussian sequences, using optimal tools from analysis on Wiener space. We apply our result to study drift parameter estimation problems for some stochastic differential equations driven by fractional Brownian motion with fixed-time-step observations.