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Integral representations of some functionals of fractional Brownian motion

By Heikki Tikanmäki

Abstract

We prove change of variables formulas [It\^o formulas] for functions of both arithmetic and geometric averages of geometric fractional Brownian motion. They are valid for all convex functions, not only for smooth ones. These change of variables formulas provide us integral representations of functions of average in the sense of generalized Lebesgue-Stieltjes integral

Topics: Mathematics - Probability, 60G22
Year: 2011
OAI identifier: oai:arXiv.org:1102.5182
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