Probability distribution solutions of a general linear equation of infinite order

Tomasz Kochanek, and Janusz Morawiec. "Probability distribution solutions of a general linear equation of infinite order." Annales Polonici Mathematici 95.2 (2009): 103-114. <http://eudml.org/doc/280914>.

@article{TomaszKochanek2009,
abstract = {Let (Ω,,P) be a probability space and let τ: ℝ × Ω → ℝ be strictly increasing and continuous with respect to the first variable, and -measurable with respect to the second variable. We obtain a partial characterization and a uniqueness-type result for solutions of the general linear equation $F(x) = ∫_\{Ω\} F(τ(x,ω))P(dω)$ in the class of probability distribution functions.},
author = {Tomasz Kochanek, Janusz Morawiec},
journal = {Annales Polonici Mathematici},
keywords = {linear functional equations; iterative functional equations; probability distribution solutions; extension of solutions; uniqueness of solutions},
language = {eng},
number = {2},
pages = {103-114},
title = {Probability distribution solutions of a general linear equation of infinite order},
url = {http://eudml.org/doc/280914},
volume = {95},
year = {2009},
}

TY - JOUR
AU - Tomasz Kochanek
AU - Janusz Morawiec
TI - Probability distribution solutions of a general linear equation of infinite order
JO - Annales Polonici Mathematici
PY - 2009
VL - 95
IS - 2
SP - 103
EP - 114
AB - Let (Ω,,P) be a probability space and let τ: ℝ × Ω → ℝ be strictly increasing and continuous with respect to the first variable, and -measurable with respect to the second variable. We obtain a partial characterization and a uniqueness-type result for solutions of the general linear equation $F(x) = ∫_{Ω} F(τ(x,ω))P(dω)$ in the class of probability distribution functions.
LA - eng
KW - linear functional equations; iterative functional equations; probability distribution solutions; extension of solutions; uniqueness of solutions
UR - http://eudml.org/doc/280914
ER -