arXiv math/06023562006-02math.PR

分数布朗运动的Molchan-Golosov表示与Mandelbrot-Van Ness表示之间的联系

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

Celine Jost

备注：: 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

摘要：

证明了分数布朗运动（fBM）的广义Molchan-Golosov积分变换与广义Mandelbrot-Van Ness积分变换之间的联系.前者通过在[0，t]上积分将任意Hurst指数K的fBm变为指数H的fBm，而后者需要在（-infty，t]上积分。

英文摘要：

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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英文摘要：

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