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Karhunen-Loeve expansion of Gaussian bridges

Pavel Chigansky
(Hebrew University, Jerusalem)
Thiele Seminar
Thursday, 4 May, 2017, at 13:15-14:00, in Koll. D (1531-211)
Abstract:
The Karhunen-Loeve theorem states that a centered process with continuous coariance function can be expanded into series of eigenfunctions of the covariance operator. This classic result is a useful tool in analysis and applications of Gaussian processes, but unfortunately the exact solutions to the eigenproblem are notoriously hard to find. In this talk I will discuss the Karhunen-Loeve expansion of Gaussian bridges. Given a “base” process, its bridge is obtained by conditioning its trajectories to start and terminate at given points. Can we find the expansion for a bridge, given the expansion for the base process? I will show show this question can be answered asymptotically for a family of processes, including the fractional Brownian motion. This is a recent joint work with M.Kleptsyna and D. Marushkevych.

Organised by: The T.N. Thiele Centre
Contact person: Mark Podolskij