Abstract
Simple upper and lower bounds are obtained for the integral ∫x0e−γttνIν(t)dt , x>0 , ν>−12 , 0<γ<1 . Most of our bounds for this integral are tight as x→∞ . We apply one of our inequalities to bound some expressions involving this integral. Two of these expressions appear in Stein's method for variance-gamma approximation, and our bounds will allow for a technical advancement to be made to the method.
| Original language | English |
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| Journal | Journal of Mathematical Analysis and Applications |
| Publication status | Accepted/In press - 30 Mar 2021 |