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Parameter estimation for fractional Brownian motion
 Hartman, Štěpán ; Kříž, Pavel (advisor) ; Čoupek, Petr (referee)
This bachelor's thesis deals with a mathematical object called fractional Brownian motion, which has substantial applications in a wide variety of disciplines including, next to theoretical and financial mathematics, the fields of biology, geography, or information technology. This concept is a generalization of a standard Brownian motion, in which we do not assume the independence of its increments. In this thesis we define said object and explore its basic properties. Subsequently, we discuss the estimators of its Hurst index. We suggest a correction of one of the methods of constructing the estimator and demonstrate its effectiveness using both simulated and real-life data. 1
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