On the connection between Molchan-Golosov and Mandelbrot-Van Ness representations of fractional Brownian motion

Details On the connection between Molchan-Golosov and Mandelbrot-Van Ness representations of fractional Brownian motion On the connection between Molchan-Golosov and Mandelbrot-Van Ness representations of fractional Brownian motion

2006-02-16

arxiv.org/abs/math/0602356v2

Mathematics

Probability

14 pages. This article can be considered as an appendix of the article "Transformation formulas for fractional Brownian motion

Scientific paper

We proof a connection between the generalized Molchan-Golosov integral
transform and the generalized Mandelbrot-Van Ness integral transform of
fractional Brownian motion (fBm). The former changes fBm of arbitrary Hurst
index K into fBm of index H by integrating over [0,t], whereas the latter
requires integration over (-infty,t].

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