On drift parameter estimation in models with fractional Brownian motion

Abstract

We consider a stochastic differential equation involving standard and fractional Brownian motion with unknown drift parameter to be estimated. We investigate the standard maximum likelihood estimate of the drift parameter, two non-standard estimates and three estimates for the sequential estimation. Model strong consistency and some other properties are proved. The linear model and Ornstein-Uhlenbeck model are studied in detail. As an auxiliary result, an asymptotic behavior of the fractional derivative of the fractional Brownian motion is established.

References in corpus (3)

• Stochastic Differential Equations Driven by Fractional Brownian Motion and Standard Brownian Motion
• Stochastic differential equation involving Wiener process and fractional Brownian motion with Hurst index $H>1/2$
• Exact maximum likelihood estimators for drift fractional Brownian motions