分数阶布朗运动的Krein spectral theory和Paley-Wiener展开
Krein's spectral theory and the Paley-Wiener expansion for fractional Brownian motion
摘要：
本文利用Krein关于单位圆上正交多项式的连续类比的工作，发展了分数布朗运动（fBM）的谱理论.我们展示的功能是正交的谱测度的fBM和获得一个显式的再生核在频域。利用这些结果，我们导出了普通布朗运动的经典Paley-Wiener展开式到分数情形的推广。
英文摘要：
In this paper we develop the spectral theory of the fractional Brownian motion (fBm) using the ideas of Krein's work on continuous analogous of orthogonal polynomials on the unit circle. We exhibit the functions which are orthogonal with respect to the spectral measure of the fBm and obtain an explicit reproducing kernel in the frequency domain. We use these results to derive an extension of the classical Paley-Wiener expansion of the ordinary Brownian motion to the fractional case.
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