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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Bronski, J.C. Small Ball Constants and Tight Eigenvalue Asymptotics for Fractional Brownian Motions. Journal of Theoretical Probability 16, 87–100 (2003). https://doi.org/10.1023/A:1022226420564
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DOI: https://doi.org/10.1023/A:1022226420564