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Estimates with weights for the characterization of the asymptotics of sums of independent random variables. (English. Ukrainian original) Zbl 0840.60042

Theory Probab. Math. Stat. 48, 131-134 (1994); translation from Teor. Jmovirn. Mat. Stat. 48, 185-190 (1993).
Summary: An estimate of the convergence of sums of geometric distributed number of independent identically distributed random variables \(\{\xi_i, i \geq 0\}\) to a function of a special form is obtained in a metric with weight as the parameter of the geometric distribution tends to 0. The case is considered where Cramér’s condition is satisfied as well as the case where \(\mathbb{E} \xi^r_0 < \infty\) for some \(r \geq 2\).

MSC:

60G50 Sums of independent random variables; random walks
60K05 Renewal theory