On the eigenproblem for Gaussian bridges

Pavel Chigansky, Marina Kleptsyna, Dmytro Marushkevych

Research output: Contribution to journalArticlepeer-review

2 Scopus citations


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.

Original languageAmerican English
Pages (from-to)1706-1726
Number of pages21
Issue number3
StatePublished - Aug 2020

Bibliographical note

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© 2020 ISI/BS


  • Eigenproblem
  • Fractional Brownian motion
  • Gaussian processes
  • Karhunen-Loève expansion


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