PIMS/AMI Seminar: Professor Yu Mishura, Kiev National University
Topic
“On drift parameter estimation in the models with long-range dependence”
Speakers
Details
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.
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.
Additional Information
For further info please see http://www.mathstats.ualberta.ca/en/Upcoming%20Events.aspx.
Professor Yu Mishura, Kiev National University
Professor Yu Mishura, Kiev National University