2000 character limit reached
On drift parameter estimation in models with fractional Brownian motion (1112.2330v1)
Published 11 Dec 2011 in math.PR and stat.ME
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.