On the eigenproblem for Gaussian bridges

Pavel Chigansky, Marina Kleptsyna, Dmytro Marushkevych

Research output: Contribution to journalArticlepeer-review

2 Scopus citations

Abstract

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
JournalBernoulli
Volume26
Issue number3
DOIs
StatePublished - Aug 2020

Bibliographical note

Publisher Copyright:
© 2020 ISI/BS

Keywords

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

Fingerprint

Dive into the research topics of 'On the eigenproblem for Gaussian bridges'. Together they form a unique fingerprint.

Cite this