Mixed fractional Brownian motion: A spectral take

P. Chigansky*, M. Kleptsyna, D. Marushkevych

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

5 Scopus citations

Abstract

This paper provides yet another look at the mixed fractional Brownian motion (fBm), this time, from the spectral perspective. The main result is an asymptotic approximation for the eigenvalues of its covariance operator. Using this approximation we derive the exact asymptotics of the L2-small ball probabilities, which was previously known only with logarithmic accuracy. The obtained expression exhibits an interesting stratification of scales, which occurs at certain values of the Hurst parameter of the fractional component. Some of them have been previously encountered in other problems involving such mixtures.

Original languageAmerican English
Article number123558
JournalJournal of Mathematical Analysis and Applications
Volume482
Issue number2
DOIs
StatePublished - 15 Feb 2020

Bibliographical note

Publisher Copyright:
© 2019 Elsevier Inc.

Keywords

  • Fractional Brownian motion
  • Gaussian processes
  • Small ball probabilities
  • Spectral problem

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