57 research outputs found
Krein's spectral theory and the Paley-Wiener expansion for fractional Brownian motion
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.Comment: Published at http://dx.doi.org/10.1214/009117904000000955 in the
Annals of Probability (http://www.imstat.org/aop/) by the Institute of
Mathematical Statistics (http://www.imstat.org
Representations of isotropic random fields with homogeneous increments, with applications to spacial fractional Brownian motion
This is a brief account of the current work by Dzhaparidze, van Zanten and Zareba, delivered as a lecture note at the conference Small deviations and related topics II held in St. Petersburg, September 12-19, 200
A large deviation result for parameter estimators and its application to nonlinear regression analysis
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