Convolutions of distributions with exponential and subexponential tails. (English) Zbl 0633.60021

Cline, Daren B. H.

J. Aust. Math. Soc., Ser. A 43, 347-365 (1987).

The author introduces a technique which allows him to obtain a number of technical results about distribution tails with a minimum of analysis. Principal among these is a real analytic proof of a theorem of J. Chover, S. Wainger and P. Ney which runs as follows:
If F is a nonnegative finite measure on \({\mathbb{R}}\), and if the tail function \(\bar F(t)=F(t,\infty)\) satisfies \(\bar F(t-u)\sim e^{au}\bar F(t)\) for all \(u\in {\mathbb{R}}\) and also \(\overline{F^*F}(t)\sim 2d \bar F(t)\), then necessarily \(d=\int e^{au} F(du)\).

Reviewer: B.Horkelheimer

MSC:

60E05

Probability distributions: general theory

Keywords:

convolution tails; exponential tails; subexponential tails; distribution tails