The law of the maximum of a bessel bridge

Abstract

Let Mδ be the maximum of a standard Bessel bridge of dimension δ. A series formula for P(Mδ ≤ a) due to Gikhman and Kiefer for δ = 1, 2, … is shown to be valid for all real δ > 0. Various other characterizations of the distribution of Mδ are given, including formulae for its Mellin transform, which is an entire function. The asymptotic distribution of Mδ is described both as δ → ∈ and as δ ↓ 0. © 1999 Applied Probability Trust.