Small-t Expansion for the Hartman-Watson Distribution

Dan Pirjol ()
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Dan Pirjol: Stevens Institute of Technology

Methodology and Computing in Applied Probability, 2021, vol. 23, issue 4, 1537-1549

Abstract: Abstract The Hartman-Watson distribution with density f r ( t ) = 1 I 0 ( r ) θ ( r , t ) $f_{r}(t)=\frac {1}{I_{0}(r)} \theta (r,t)$ with r > 0 is a probability distribution defined on t ∈ ℝ + $t \in \mathbb {R}_{+}$ , which appears in several problems of applied probability. The density of this distribution is given by an integral θ(r, t) which is difficult to evaluate numerically for small t → 0. Using saddle point methods, we obtain the first two terms of the t → 0 expansion of θ(ρ/t, t) at fixed ρ > 0.

Keywords: Asymptotic expansions; Saddle point method; Hartman-Watson distribution; 41A60; 33F05; 60-08 (search for similar items in EconPapers)
Date: 2021
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DOI: 10.1007/s11009-020-09827-5

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