From invariance under binomial thinning to unification of the Cauchy and the Gołąb-Schinzel-type equations
Karol Baron, Jacek Wesołowski · arXiv (Cornell University) · 2021
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 Gołab-Schinzel equation. We solve these equations in several settings with no or mild regularity assumptions imposed on unknown functions.