Abstract
Simple inequalities are established for some integrals involving the modified
Bessel functions of the first and second kind. In most cases, we show that we
obtain the best possible constant or that our bounds are tight in certain limits. We
apply these inequalities to obtain uniform bounds for several expressions involving
integrals of modified Bessel functions. Such expressions occur in Stein’s method
for variance-gamma approximation, and the results obtained in this paper allow for
technical advances in the method. We also present some open problems that arise
from this research.
Bessel functions of the first and second kind. In most cases, we show that we
obtain the best possible constant or that our bounds are tight in certain limits. We
apply these inequalities to obtain uniform bounds for several expressions involving
integrals of modified Bessel functions. Such expressions occur in Stein’s method
for variance-gamma approximation, and the results obtained in this paper allow for
technical advances in the method. We also present some open problems that arise
from this research.
| Original language | English |
|---|---|
| Pages (from-to) | 172-190 |
| Journal | Journal of Mathematical Analysis and Applications |
| Volume | 462 |
| Early online date | 6 Feb 2018 |
| DOIs | |
| Publication status | Published - Jun 2018 |