Journal of Theoretical Probability

, Volume 16, Issue 1, pp 87–100

Small Ball Constants and Tight Eigenvalue Asymptotics for Fractional Brownian Motions

  • Jared C. Bronski

DOI: 10.1023/A:1022226420564

Cite this article as:
Bronski, J.C. Journal of Theoretical Probability (2003) 16: 87. doi:10.1023/A:1022226420564


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 L2 ball estimates for fractional Brownian motions follows in a straightforward way.

Fractional Brownian motionsmall ball probabilitieseigenvalue asymptoticsKarhunen–Loeve expansion

Copyright information

© Plenum Publishing Corporation 2003

Authors and Affiliations

  • Jared C. Bronski

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