The rate of convergence of estimate for Hurst index of fractional Brownian motion involved into stochastic differential equation

TL;DR

This paper investigates the convergence rate of estimators for the Hurst index in stochastic differential equations driven by fractional Brownian motion, using quadratic variations of observed solutions.

Contribution

It provides new estimates for the Hurst parameter and establishes their convergence rates within the context of fractional Brownian motion-driven SDEs.

Findings

Derived estimates for the Hurst parameter

Established convergence rates of the estimators

Validated the approach through theoretical analysis

Abstract

We consider stochastic differential equation involving pathwise integral with respect to fractional Brownian motion. The estimates for the Hurst parameter are constructed according to first- and second-order quadratic variations of observed values of the solution. The rate of convergence of these estimates to the true value of a parameter is established.