The set of probability distribution solutions of a linear functional equation
Tom 93 / 2008
Annales Polonici Mathematici 93 (2008), 253-261
MSC: Primary 39B12; Secondary 39B22.
DOI: 10.4064/ap93-3-6
Streszczenie
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.
