Probability distribution solutions of a general linear equation
of infinite order
Annales Polonici Mathematici, Tome 95 (2009) no. 2, pp. 103-114
Voir la notice de l'article provenant de la source Institute of Mathematics Polish Academy of Sciences
\def{\mit\Omega}{{\mit\Omega}}Let $({\mit\Omega}, {\mathcal A},P)$ be a probability space and let
$\tau\colon\mathbb R\times{\mit\Omega}\to\mathbb R$ be
strictly increasing and continuous with respect to the first variable,
and ${\cal A}$-measurable with respect to the second variable.
We obtain a partial characterization and a uniqueness-type result
for solutions
of the general linear equation
$$
F(x)=\int_{\mit\Omega} F(\tau (x,\omega ))P(d\omega )
$$
in the class of probability distribution functions.
Keywords:
def mit omega mit omega mit omega mathcal probability space tau colon mathbb times mit omega mathbb strictly increasing continuous respect first variable cal measurable respect second variable obtain partial characterization uniqueness type result solutions general linear equation int mit omega tau omega omega class probability distribution functions
Affiliations des auteurs :
Tomasz Kochanek 1 ; Janusz Morawiec 1
@article{10_4064_ap95_2_1,
author = {Tomasz Kochanek and Janusz Morawiec},
title = {Probability distribution solutions of a general linear equation
of infinite order},
journal = {Annales Polonici Mathematici},
pages = {103--114},
publisher = {mathdoc},
volume = {95},
number = {2},
year = {2009},
doi = {10.4064/ap95-2-1},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/10.4064/ap95-2-1/}
}
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 SP - 103 EP - 114 VL - 95 IS - 2 PB - mathdoc UR - http://geodesic.mathdoc.fr/articles/10.4064/ap95-2-1/ DO - 10.4064/ap95-2-1 LA - en ID - 10_4064_ap95_2_1 ER -
%0 Journal Article %A Tomasz Kochanek %A Janusz Morawiec %T Probability distribution solutions of a general linear equation of infinite order %J Annales Polonici Mathematici %D 2009 %P 103-114 %V 95 %N 2 %I mathdoc %U http://geodesic.mathdoc.fr/articles/10.4064/ap95-2-1/ %R 10.4064/ap95-2-1 %G en %F 10_4064_ap95_2_1
Tomasz Kochanek; Janusz Morawiec. Probability distribution solutions of a general linear equation of infinite order. Annales Polonici Mathematici, Tome 95 (2009) no. 2, pp. 103-114. doi: 10.4064/ap95-2-1
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