Fractional Brownian Motion with Variable Hurst Parameter. - Ryvkina, Jelena. (2017)
Abstract: A new class of Gaussian processes generalizing the usual fractional Brownian motion for Hurst indices in (1/2,1) is presented. Any measurable function assuming values in this interval can now be chosen as a parameter. These new processes allow for modeling of phenomena where the regularity properties change with time, such as in the volatility of a stock or in internet traffic. Some properties of the paths, including long-range dependence and Hoelder continuity under regularity assumptions on the parameter function, are discussed.; Thesis (Ph.D.)--Tufts University, 2013.; Submitted to the Dept. of Mathematics.; Advisor: Marjorie Hahn.; Committee: Boris Hasselblatt, and Evarist Gine-Masdeu.; Keyword: Mathematics.