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 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.
Bibliographical noteFunding Information:
We are grateful to A.I. Nazarov for bringing our attention to several related works, including  and . This work has been supported by the ISF grant 558/13.
© 2020 ISI/BS
- Fractional Brownian motion
- Gaussian processes
- Karhunen-Loève expansion