This paper is concerned with large 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 -rates.
Cite this article
Paul L. Butzer, D. Schulz, General Random Sum Limit Theorems for Martingales with large -Rates. Z. Anal. Anwend. 2 (1983), no. 2, pp. 97–109DOI 10.4171/ZAA/52