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• W2959650376 abstract "Given a nonincreasing null sequence $$T = (T_j)_{j geqslant 1}$$ of nonnegative random variables satisfying some classical integrability assumptions and $${mathbb {E}}(sum _{j}T_{j}^{alpha })=1$$ for some $$alpha >0$$ , we characterize the solutions of the well-known functional equation $$begin{aligned} f(t),=,textstyle {mathbb {E}}left( prod _{jgeqslant 1}f(tT_{j})right) ,quad tgeqslant 0, end{aligned}$$ related to the so-called smoothing transform and its min-type variant. In order to do so within the class of nonnegative and nonincreasing functions, we provide a new three-step method whose merits are that" @default.
• W2959650376 created "2019-07-23" @default.
• W2959650376 creator A5090416415 @default.
• W2959650376 creator A5090566468 @default.
• W2959650376 date "2022-01-09" @default.
• W2959650376 modified "2023-10-01" @default.
• W2959650376 title "A Simple Method to Find All Solutions to the Functional Equation of the Smoothing Transform" @default.
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• W2959650376 doi "https://doi.org/10.1007/s10959-021-01151-z" @default.
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