# Probability distribution solutions of a general linear equation of infinite order

Tomasz Kochanek; Janusz Morawiec

Annales Polonici Mathematici (2009)

- Volume: 95, Issue: 2, page 103-114
- ISSN: 0066-2216

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topTomasz 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 -

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