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math.PR2025
Orthogonal series for si- and related processes, Karhunen-Loève decompositions
Kacha Dzhaparidze
This paper reproduces results from Chapter 11 of the forthcoming book \cite{dzh25}. It discusses series expansions of processes with stationary increments (si-processes) and certai…
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…