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Zeitschrift für Analysis und ihre Anwendungen


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Volume 2, Issue 2, 1983, pp. 97–109
DOI: 10.4171/ZAA/52

Published online: 1983-04-30

General Random Sum Limit Theorems for Martingales with large $\mathcal O$-Rates

Paul L. Butzer[1] and D. Schulz[2]

(1) Rheinisch-Westfälische Technische Hochschule Aachen, Germany
(2) Rheinisch-Westfälische Technische Hochschule Aachen, Germany

This paper is concerned with large $\mathcal O$ error estimates for convergence in distribution of random sums of not necessarily independent random variables. As applications of a general theorem one obtains the random-sum versions of the central limit theorem and of the weak law of large numbers for martingale difference sequences by specializing the limiting random variable. Both theorems are equipped with $\mathcal O$-rates.

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Butzer Paul , Schulz D.: General Random Sum Limit Theorems for Martingales with large $\mathcal O$-Rates. Z. Anal. Anwend. 2 (1983), 97-109. doi: 10.4171/ZAA/52