Small Ball Constants and Tight Eigenvalue Asymptotics for Fractional Brownian Motions

Jared C. Bronski ()

Journal of Theoretical Probability, 2003, vol. 16, issue 1, 87-100

Abstract: 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.

Keywords: Fractional Brownian motion; small ball probabilities; eigenvalue asymptotics; Karhunen–Loeve expansion (search for similar items in EconPapers)
Date: 2003
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DOI: 10.1023/A:1022226420564

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