Small-t Expansion for the Hartman-Watson Distribution

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Abstract

The Hartman-Watson distribution with density fr(t)=1I0(r)θ(r,t) with r > 0 is a probability distribution defined on t∈ 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.

Original languageEnglish
Pages (from-to)1537-1549
Number of pages13
JournalMethodology and Computing in Applied Probability
Volume23
Issue number4
DOIs
StatePublished - Dec 2021

Keywords

  • Asymptotic expansions
  • Hartman-Watson distribution
  • Saddle point method

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