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