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

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:

 6e+06 Probability distributions: general theory