On drift parameter estimation in models with fractional Brownian motion

Details On drift parameter estimation in models with fractional Brownian motion On drift parameter estimation in models with fractional Brownian motion

2011-12-11

arxiv.org/abs/1112.2330v1

Mathematics

Probability

Scientific paper

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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