Small Ball Constants and Tight Eigenvalue Asymptotics for Fractional Brownian Motions

Research output: Contribution to journalArticle

Abstract

In this paper we prove rigorous large n asymptotics for the Karhunen-Loeve eigenvalues of a fractional Brownian motion. From the asymptotics of the eigenvalues the exact constants for small L 2 ball estimates for fractional Brownian motions follows in a straightforward way.

Original languageEnglish (US)
Pages (from-to)87-100
Number of pages14
JournalJournal of Theoretical Probability
Volume16
Issue number1
DOIs
StatePublished - Jan 1 2003

Keywords

  • Eigen-value asymptotics
  • Fractional Brownian motion
  • Karhunen-Loeve expansion
  • Small ball probabilities

ASJC Scopus subject areas

  • Statistics and Probability
  • Mathematics(all)
  • Statistics, Probability and Uncertainty

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