From invariance under binomial thinning to unification of the Cauchy and the Gołąb- Schinzel-type equations
| Autor: | Jacek Wesołowski, Karol Baron |
|---|---|
| Jazyk: | angličtina |
| Rok vydání: | 2021 |
| Předmět: |
Power series
Unification Binomial (polynomial) Applied Mathematics power series family 010102 general mathematics binomial thinning Cauchy distribution 010103 numerical & computational mathematics Type (model theory) 01 natural sciences Connection (mathematics) Gołąb–Schinzel equation Mathematics (miscellaneous) Cauchy equation Applied mathematics Probability distribution Point (geometry) 0101 mathematics Mathematics |
| Popis: | 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 Gołąb–Schinzel equation. We solve these equations in several settings with no or mild regularity assumptions imposed on unknown functions. |
| Databáze: | OpenAIRE |
| Externí odkaz: |
|