On inference for fractional differential equations

TL;DR

This paper develops a method to estimate parameters in fractional differential equations driven by fractional Brownian motion, providing convergence rates and demonstrating effective numerical estimation.

Contribution

It introduces a maximum likelihood type estimator for fractional differential equations using Malliavin calculus, with proven convergence rates and practical numerical validation.

Findings

Estimator achieves accurate parameter estimation.

Convergence rates are established for the approximation.

Numerical experiments confirm the method's effectiveness.

Abstract

Based on Malliavin calculus tools and approximation results, we show how to compute a maximum likelihood type estimator for a rather general differential equation driven by a fractional Brownian motion with Hurst parameter H>1/2. Rates of convergence for the approximation task are provided, and numerical experiments show that our procedure leads to good results in terms of estimation.