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math.PR2005★ 23 cited
Donsker theorems for diffusions: Necessary and sufficient conditions
Aad van der Vaart, Harry van Zanten
We consider the empirical process G_t of a one-dimensional diffusion with finite speed measure, indexed by a collection of functions F. By the central limit theorem for diffusions,…
math.PR2005★ 34 cited
Krein's spectral theory and the Paley-Wiener expansion for fractional Brownian motion
Kacha Dzhaparidze, Harry van Zanten
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 c…