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Little's theorem: A stochastic integral approach

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Abstract

In a previous paper we have given a unified approach to the PASTA and the conditional PASTA property that is based upon the observation that the difference between the two limits can be represented as a stochastic integral with respect to a square integrable martingale. The equality of the two limits is then a consequence of a strong law of large numbers for martingales. In this paper we derive a non-standard version of Little's theorem via the same method. The moral of the story is that each of these theorems is but a particular case of a more general theory.

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Rosenkrantz, W.A. Little's theorem: A stochastic integral approach. Queueing Syst 12, 319–324 (1992). https://doi.org/10.1007/BF01158806

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  • DOI: https://doi.org/10.1007/BF01158806

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