Estimation of parameters of SDE driven by fractional Brownian motion with polynomial drift

TL;DR

This paper proposes strongly consistent and asymptotically normal estimators for the Hurst index and volatility in SDEs driven by fractional Brownian motion, using discrete data observations.

Contribution

It introduces new estimators for key parameters of SDEs with polynomial drift driven by fractional Brownian motion, ensuring consistency and normality.

Findings

Estimators are strongly consistent.

Estimators are asymptotically normal.

Effective for discrete observations.

Abstract

Strongly consistent and asymptotically normal estimators of the Hurst index and volatility parameters of solutions of stochastic differential equations with polynomial drift are proposed. The estimators are based on discrete observations of the underlying processes.