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arXiv · 1706.00187

A natural probability measure derived from Stern's diatomic sequence

Michael Baake·Michael Coons
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Abstract

Stern's diatomic sequence with its intrinsic repetition and refinement structure between consecutive powers of $2$ gives rise to a rather natural probability measure on the unit interval. We construct this measure and show that it is purely singular continuous, with a strictly increasing, H\"older continuous distribution function. Moreover, we relate this function with the solution of the dilation equation for Stern's diatomic sequence.

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Michael Baake, Michael Coons. 2017-06-01. A natural probability measure derived from Stern's diatomic sequence. https://arxiv.org/abs/1706.00187

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