Integral representations of some functionals of fractional Brownian motion

Details Integral representations of some functionals of fractional Brownian motion Integral representations of some functionals of fractional Brownian motion

2011-02-25

arxiv.org/abs/1102.5182v2

Mathematics

Probability

Scientific paper

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.

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