JournalszaaVol. 2, No. 2pp. 97–109

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

  • Paul L. Butzer

    Rheinisch-Westfälische Technische Hochschule Aachen, Germany
  • D. Schulz

    Rheinisch-Westfälische Technische Hochschule Aachen, Germany
General Random Sum Limit Theorems for Martingales with large $\mathcal O$-Rates cover
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Abstract

This paper is concerned with large O\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 O\mathcal O-rates.

Cite this article

Paul L. Butzer, D. Schulz, General Random Sum Limit Theorems for Martingales with large O\mathcal O-Rates. Z. Anal. Anwend. 2 (1983), no. 2, pp. 97–109

DOI 10.4171/ZAA/52