The maximum likelihood type estimator of SDEs with fractional Brownian motion under small noise asymptotics in the rough case

TL;DR

This paper develops a maximum likelihood estimator for parameters in stochastic differential equations driven by fractional Brownian motion, analyzing its asymptotic properties as noise diminishes in the rough case.

Contribution

It introduces a new estimator for SDEs with fractional Brownian motion and proves its asymptotic normality under small noise conditions.

Findings

Estimator is asymptotically normal.

Convergence of moments established.

Applicable in rough fractional Brownian motion scenarios.

Abstract

We study the problem of parametric estimation for continuously observed stochastic differential equation driven by fractional Brownian motion. Under some assumptions on drift and diffusion coefficients, we construct maximum likelihood estimator and establish its the asymptotic normality and moment convergence of the drift parameter when a small dispersion coefficient vanishes.