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The set of probability distribution solutions of a linear functional equation

Tom 93 / 2008

Janusz Morawiec, Ludwig Reich 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.

Autorzy

  • Janusz MorawiecInstitute of Mathematics
    Silesian University
    Bankowa 14
    40-007 Katowice, Poland
    e-mail
  • Ludwig ReichInstitut für Mathematik
    Karl Franzens Universität
    Heinrichstrasse 36
    A-8010 Graz, Austria
    e-mail

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