TY - JOUR
T1 - Small-t Expansion for the Hartman-Watson Distribution
AU - Pirjol, Dan
N1 - Publisher Copyright:
© 2020, Springer Science+Business Media, LLC, part of Springer Nature.
PY - 2021/12
Y1 - 2021/12
N2 - 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.
AB - 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.
KW - Asymptotic expansions
KW - Hartman-Watson distribution
KW - Saddle point method
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U2 - 10.1007/s11009-020-09827-5
DO - 10.1007/s11009-020-09827-5
M3 - Article
AN - SCOPUS:85092411198
SN - 1387-5841
VL - 23
SP - 1537
EP - 1549
JO - Methodology and Computing in Applied Probability
JF - Methodology and Computing in Applied Probability
IS - 4
ER -