Abstract

This chapter gives a synoptic view of limit theorems for Maximal Random Sums. The obtained results are not only of theoretical interest but are also very important in various applications, in the theory of Markov chains, in sequential analysis, in random walk problems, in connection with Monte Carlo methods, and in the theory of queues. The present paper establishes some theorems concerning the limit behavior of sequences in the case where no assumptions concerning the interdependence between the random indices and the terms are made.

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