On a Functional Equation Characterizing Some Probability Distributions

On a Functional Equation Characterizing Some Probability Distributions

We find all nonnegative solutions f of the equation f x = ∏ j = 1 n f s j x p j , defined in a one-sided vicinity of 0 and having a prescribed asymptotic at 0 . The main theorem extends a result obtained by J. A. Baker [ Proc. Amer. Math. Soc. , 121 , 767 (1994)].

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Veröffentlicht in:Ukrainian mathematical journal 2024, Vol.76 (1), p.112-121
Hauptverfasser: Jarczyk, Justyna, Jarczyk, Witold
Format: Artikel
Sprache:eng
Schlagworte:
Algebra
Analysis
Applications of Mathematics
Functional equations
Geometry
Mathematics
Mathematics and Statistics
Statistics
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Zusammenfassung:We find all nonnegative solutions f of the equation f x = ∏ j = 1 n f s j x p j , defined in a one-sided vicinity of 0 and having a prescribed asymptotic at 0 . The main theorem extends a result obtained by J. A. Baker [ Proc. Amer. Math. Soc. , 121 , 767 (1994)].
ISSN:0041-5995
1573-9376
DOI:10.1007/s11253-024-02311-0