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arXiv · 2106.08665

From invariance under binomial thinning to unification of the Cauchy and the Go{\l}\k{a}b-Schinzel-type equations

Karol Baron·Jacek Wesołowski
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Abstract

We point out to a connection between a problem of invariance of power series families of probability distributions under binomial thinning and functional equations which generalize both the Cauchy and an additive form of the Go{\l}ab-Schinzel equation. We solve these equations in several settings with no or mild regularity assumptions imposed on unknown functions.

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Karol Baron, Jacek Wesołowski. 2021-06-16. From invariance under binomial thinning to unification of the Cauchy and the Go{\l}\k{a}b-Schinzel-type equations. https://arxiv.org/abs/2106.08665

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