arXiv:math/0602356 Abstract

arXiv:math/0602356 [math.PR]Abstract References Reviews Resources

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

Published 2006-02-16, updated 2007-05-04Version 2

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].

Comments: 14 pages. This article can be considered as an appendix of the article "Transformation formulas for fractional Brownian motion" by C. Jost (published in Stochastic Processes and their Applications). The title changed slightly from v1 to v2. The v2 is the final version and will appear in the Journal of Integral Equations and Applications

Categories: math.PR

Subjects: 60G15, 26A33, 60G18

Keywords: fractional brownian motion, mandelbrot-van ness representations, connection, generalized mandelbrot-van ness integral transform, generalized molchan-golosov integral transform

Related articles: Most relevant | Search more

arXiv:math/0310413 [math.PR] (Published 2003-10-26)

Unilateral Small Deviations for the Integral of Fractional Brownian Motion

G. Molchan, A. Khokhlov

arXiv:math/0509353 [math.PR] (Published 2005-09-15)

Approximation of rough paths of fractional Brownian motion

Annie Millet, Marta Sanz-Solé

arXiv:math/0503656 [math.PR] (Published 2005-03-29)

Krein's spectral theory and the Paley-Wiener expansion for fractional Brownian motion