Robert E. Gaunt

activity

20182025

collaborators

Showing 2018Show all

7 papers · 1 filter

math.CA2018

Inequalities for integrals of the modified Struve function of the first kind II

Robert E. Gaunt

Simple inequalities are established for integrals of the type $\int_{0}^{x} e^{- γ t} t^{- ν} L_{ν} (t) d t$ , where $x > 0$ , $0 \leq γ < 1$ , $ν > - \frac{3}{2}$ and $\mathb…

math.ST2018

A note on the distribution of the product of zero mean correlated normal random variables

Robert E. Gaunt

The problem of finding an explicit formula for the probability density function of two zero mean correlated normal random variables dates back to 1936. Perhaps surprisingly, this p…

math.CA2018

Inequalities for some integrals involving modified Bessel functions

Robert E. Gaunt

Simple inequalities are established for some integrals involving the modified Bessel functions of the first and second kind. In most cases these inequalities are tight in certain l…

math.PR2018

Stein operators for variables form the third and fourth Wiener chaoses

Robert E. Gaunt

Let $Z$ be a standard normal random variable and let $H_{n}$ denote the $n$ -th Hermite polynomial. In this note, we obtain Stein equations for the random variables $H_{3} (Z)$ and $H_4(…

math.PR2018

Stein's Method for the Single Server Queue in Heavy Traffic

Robert E. Gaunt, Neil Walton

Following recent developments in the application of Stein's method in queueing theory, this paper is intended to be a short treatment showing how Stein's method can be developed an…

math.CA2018

Bounds for modified Struve functions of the first kind and their ratios

Robert E. Gaunt

We obtain a simple two-sided inequality for the ratio $L_{ν} (x) / L_{ν - 1} (x)$ in terms of the ratio $I_{ν} (x) / I_{ν - 1} (x)$ , where $L_{ν} (x)$ is the modified Struv…