On drift parameter estimation in models with fractional Brownian motion

2011/12/11 by Kozachenko, Yuriy, Melnikov, Alexander, Mishura, Yuliya
#FOS: Computer and information sciences #FOS: Mathematics #Methodology (stat.ME) #Probability (math.PR)

paper · doi:10.48550/arxiv.1112.2330

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.

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