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On the eigenproblem for Gaussian bridges
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Spectral decomposition of the covariance operator is one of the main building blocks in the theory and applications of Gaussian processes. Unfortunately it is notoriously hard to derive in a closed form. In this paper we consider the eigenproblem for Gaussian bridges. Given a {\em base} process, its bridge is obtained by conditioning the trajectories to start and terminate at the given points. What can be said about the spectrum of a bridge, given the spectrum of its base process? We show how this question can be answered asymptotically for a family of processes, including the fractional Brownian motion.
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Spectral asymptotics for a class of integro-differential equations arising in the theory of fractional Gaussian processes
For fractional Gaussian covariance operators satisfying (K_alpha psi)(x) = -lambda psi''(x), the eigenvalues obey lambda_n = C (pi n - c_alpha - kappa pi/(3-alpha) + O(n^{-1}))^{alpha-3}, and the same formula persists...
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