Summary
Rather general versions of the Erdős-Rényi [6] new law of large numbers have recently been given by S. Csörgő [5] for sequences of rv's which have stationary and independent increments and satisfy a first order large deviation theorem. It is shown that Csörgő's results can be extended to cover also situations of stochastic processes where stationarity and independence of increments are not generally available, but for randomly chosen subsequences of the process. Examples demonstrate that the main result can be applied, for instance, to waiting-times in G/G/1 queuing models or cumulative processes in renewal theory, where Erdős-Rényi type laws cannot be derived from Csörgő's theorems.
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Steinebach, J. On general versions of Erdős-Rényi laws. Z. Wahrscheinlichkeitstheorie verw Gebiete 56, 549–554 (1981). https://doi.org/10.1007/BF00531433
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DOI: https://doi.org/10.1007/BF00531433