Geodesic
The set of probability distribution solutions of a linear functional equation
Janusz Morawiec1 ; Ludwig Reich2
1 Institute of Mathematics Silesian University Bankowa 14 40-007 Katowice, Poland
2 Institut für Mathematik Karl Franzens Universität Heinrichstrasse 36 A-8010 Graz, Austria
Annales Polonici Mathematici, Tome 93 (2008) no. 3, pp. 253-261.

Voir la notice de l'article provenant de la source Institute of Mathematics Polish Academy of Sciences

Let $({\mit\Omega}, {\mathcal A}, P)$ be a probability space and let $\tau\colon\mathbb R\times{\mit\Omega}\to\mathbb R$ be a function which is strictly increasing and continuous with respect to the first variable, measurable with respect to the second variable. Given the set of all continuous probability distribution solutions of the equation $$ F(x)=\int_{{\mit\Omega}}F(\tau(x,\omega))\,dP(\omega) $$ we determine the set of all its probability distribution solutions.
DOI : 10.4064/ap93-3-6
Keywords: mit omega mathcal probability space tau colon mathbb times mit omega mathbb function which strictly increasing continuous respect first variable measurable respect second variable given set continuous probability distribution solutions equation int mit omega tau omega omega determine set its probability distribution solutions

Janusz Morawiec 1 ; Ludwig Reich 2

1 Institute of Mathematics Silesian University Bankowa 14 40-007 Katowice, Poland
2 Institut für Mathematik Karl Franzens Universität Heinrichstrasse 36 A-8010 Graz, Austria 
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Janusz Morawiec; Ludwig Reich. The set of probability distribution solutions
of a linear functional equation. Annales Polonici Mathematici, Tome 93 (2008) no. 3, pp. 253-261. doi : 10.4064/ap93-3-6. http://geodesic.mathdoc.fr/articles/10.4064/ap93-3-6/

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