Probability distribution solutions of a general linear equation of infinite order

Tomasz Kochanek¹ ; Janusz Morawiec¹

¹Institute of Mathematics Silesian University Bankowa 14 40-007 Katowice, Poland

Annales Polonici Mathematici, Tome 95 (2009) no. 2, pp. 103-114

Résumé

\def{\mit\Omega}{{\mit\Omega}}Let $({\mit\Omega}, {\mathcal A},P)$ be a probability space and let $\tau\colon\mathbb R\times{\mit\Omega}\to\mathbb R$ be strictly increasing and continuous with respect to the first variable, and ${\cal A}$-measurable with respect to the second variable. We obtain a partial characterization and a uniqueness-type result for solutions of the general linear equation $$ F(x)=\int_{\mit\Omega} F(\tau (x,\omega ))P(d\omega ) $$ in the class of probability distribution functions.

Détail

DOI : 10.4064/ap95-2-1

Keywords: def mit omega mit omega mit omega mathcal probability space tau colon mathbb times mit omega mathbb strictly increasing continuous respect first variable cal measurable respect second variable obtain partial characterization uniqueness type result solutions general linear equation int mit omega tau omega omega class probability distribution functions