Exponential asymptotics of sums of a geometric number of independent random variables. (English. Russian original) Zbl 0748.60042

Sugakova, E. V.

Theory Probab. Math. Stat. 42, 161-166 (1991); translation from Teor. Veroyatn. Mat. Stat., Kiev 42, 135-139 (1990).

For a sequence \(\{ \xi_ i, i\geq 0\}\) of positive independent identically distributed random variables without finite second moment the uniform convergence of distributions of sums with geometrically distributed summation index to the exponential distribution is estimated in case \(\text{E}\xi_ 0^ \alpha <\infty\) for some \(1<\alpha <2\).

Reviewer: N.Kalinauskaitė (Vilnius)

MSC:

60G50	Sums of independent random variables; random walks
60F05	Central limit and other weak theorems

Keywords:

uniform convergence; distributions of sums with geometrically distributed summation index; exponential distribution