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Small Ball Constants and Tight Eigenvalue Asymptotics for Fractional Brownian Motions

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  • Jared C. Bronski

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.

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  • Jared C. Bronski, 2003. "Small Ball Constants and Tight Eigenvalue Asymptotics for Fractional Brownian Motions," Journal of Theoretical Probability, Springer, vol. 16(1), pages 87-100, January.
    • Handle: RePEc:spr:jotpro:v:16:y:2003:i:1:d:10.1023_a:1022226420564
    DOI: 10.1023/A:1022226420564
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    References listed on IDEAS

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    1. Wang, Yazhen, 1997. "Small ball problem via wavelets for Gaussian processes," Statistics & Probability Letters, Elsevier, vol. 32(2), pages 133-139, March.
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    Cited by:

    1. Steffen Dereich, 2003. "Small Ball Probabilities Around Random Centers of Gaussian Measures and Applications to Quantization," Journal of Theoretical Probability, Springer, vol. 16(2), pages 427-449, April.

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