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arXiv · 0704.0398

Renewals for exponentially increasing lifetimes, with an application to digital search trees

Florian Dennert·Rudolf Grübel
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Abstract

We show that the number of renewals up to time $t$ exhibits distributional fluctuations as $t\to\infty$ if the underlying lifetimes increase at an exponential rate in a distributional sense. This provides a probabilistic explanation for the asymptotics of insertion depth in random trees generated by a bit-comparison strategy from uniform input; we also obtain a representation for the resulting family of limit laws along subsequences. Our approach can also be used to obtain rates of convergence.

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Florian Dennert, Rudolf Grübel. 2007-04-03. Renewals for exponentially increasing lifetimes, with an application to digital search trees. https://doi.org/10.1214/105051606000000862

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