On a subclass of regularly varying functions
The author studies positive measurable functions \(f,a\) for which \(\displaystyle\lim \sup_{t \to \infty} | f(x + t) - f(t) |/a(t) < \infty\), or \(\displaystyle\lim_{t \to \infty}\) \((f(x + t) - f(t))/a(t) = \mu(x)\) exists, for all \(x \geq 0\). This is useful in studying asymptotic behaviour of the convolution product of functions. The probability application is to extreme value theory, and second-order results for subexponential distribution functions.
asymptotic behaviour of the convolution product of functions
scientific article; zbMATH DE number 758086
scientific article