# The set of probability distribution solutions of a linear functional equation

• Volume: 93, Issue: 3, page 253-261
• ISSN: 0066-2216

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## Abstract

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Let (Ω,,P) be a probability space and let τ: ℝ×Ω → 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 $F\left(x\right)={\int }_{\Omega }F\left(\tau \left(x,\omega \right)\right)dP\left(\omega \right)$ we determine the set of all its probability distribution solutions.

## How to cite

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Janusz Morawiec, and Ludwig Reich. "The set of probability distribution solutions of a linear functional equation." Annales Polonici Mathematici 93.3 (2008): 253-261. <http://eudml.org/doc/280708>.

@article{JanuszMorawiec2008,
abstract = {Let (Ω,,P) be a probability space and let τ: ℝ×Ω → 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 $F(x) = ∫_\{Ω\} F(τ(x,ω))dP(ω)$ we determine the set of all its probability distribution solutions.},
author = {Janusz Morawiec, Ludwig Reich},
journal = {Annales Polonici Mathematici},
keywords = {integro-functional equations; probability distribution functions},
language = {eng},
number = {3},
pages = {253-261},
title = {The set of probability distribution solutions of a linear functional equation},
url = {http://eudml.org/doc/280708},
volume = {93},
year = {2008},
}

TY - JOUR
AU - Janusz Morawiec
AU - Ludwig Reich
TI - The set of probability distribution solutions of a linear functional equation
JO - Annales Polonici Mathematici
PY - 2008
VL - 93
IS - 3
SP - 253
EP - 261
AB - Let (Ω,,P) be a probability space and let τ: ℝ×Ω → 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 $F(x) = ∫_{Ω} F(τ(x,ω))dP(ω)$ we determine the set of all its probability distribution solutions.
LA - eng
KW - integro-functional equations; probability distribution functions
UR - http://eudml.org/doc/280708
ER -

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