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Probability distribution solutions of a general linear equation of infinite order

Tomasz Kochanek, Janusz Morawiec (2009)

Annales Polonici Mathematici

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 ( d ω ) in the class of probability distribution functions.

Probability distribution solutions of a general linear equation of infinite order, II

Tomasz Kochanek, Janusz Morawiec (2010)

Annales Polonici Mathematici

Let (Ω,,P) be a probability space and let τ: ℝ × Ω → ℝ be a mapping strictly increasing and continuous with respect to the first variable, and -measurable with respect to the second variable. We discuss the problem of existence of probability distribution solutions of the general linear equation F ( x ) = Ω F ( τ ( x , ω ) ) P ( d ω ) . We extend our uniqueness-type theorems obtained in Ann. Polon. Math. 95 (2009), 103-114.

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