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

Volume 99 / 2010

Tomasz Kochanek, Janusz Morawiec Annales Polonici Mathematici 99 (2010), 215-224 MSC: Primary 60E05, 39B12; Secondary 39B22. DOI: 10.4064/ap99-3-1

Abstract

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.

Authors

  • Tomasz KochanekInstitute of Mathematics
    Silesian University
    40-007 Katowice, Poland
    e-mail
  • Janusz MorawiecInstitute of Mathematics
    Silesian University
    40-007 Katowice, Poland
    e-mail

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