Probability distribution solutions of a general linear equation of infinite order
Volume 95 / 2009
Annales Polonici Mathematici 95 (2009), 103-114
DOI: 10.4064/ap95-2-1
Abstract
\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.
