Probability distribution solutions of a general linear equation of infinite order, II

Tomasz Kochanek¹ ; Janusz Morawiec¹

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

Annales Polonici Mathematici, Tome 99 (2010) no. 3, pp. 215-224

Résumé

Let $(\Omega, {\cal A},P)$ be a probability space and let $\tau\colon\mathbb R\times\Omega\to\mathbb R$ be a mapping strictly increasing and continuous with respect to the first variable, and ${\cal A}$-measurable with respect to the second variable. We discuss the problem of existence of probability distribution solutions of the general linear equation $$ F(x)=\int\limits_\Omega F (\tau (x,\omega )) \, P(d\omega ). $$ We extend our uniqueness-type theorems obtained in Ann. Polon. Math. 95 (2009), 103–114.

Détail

DOI : 10.4064/ap99-3-1

Keywords: omega cal probability space tau colon mathbb times omega mathbb mapping strictly increasing continuous respect first variable cal measurable respect second variable discuss problem existence probability distribution solutions general linear equation int limits omega tau omega omega extend uniqueness type theorems obtained ann polon math