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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 ... read moreproperties 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.read less
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