A probabilistic note on the Cauchy functional equation

DOI10.1007/s00010-018-0575-2zbMath1408.39020OpenAlexW2811233340WikidataQ129645388 ScholiaQ129645388MaRDI QIDQ1736316

Sergey N. Smirnov

Publication date: 26 March 2019

Published in: Aequationes Mathematicae (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s00010-018-0575-2

zbMATH Keywords

characteristic functionnormal distributionmeasurabilityCauchy functional equationlocal integrabilityBernstein's characterization theorem

Mathematics Subject Classification ID

Characteristic functions; other transforms (60E10) Functional equations for real functions (39B22) Characterization and structure theory of statistical distributions (62E10)

Related Items (6)

A probabilistic method of solving Lobachevsky's functional equation ⋮ Functional equations for the stochastic exponential ⋮ Martingale transformations of Brownian motion with application to functional equations ⋮ On martingale transformations of multidimensional Brownian motion ⋮ Non-existence of measurable solutions of certain functional equations via probabilistic approaches ⋮ Functional equations and martingales

Cites Work

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• Remarks on the Cauchy functional equation and variations of it
• Erdős problem and quadratic equation
• Regularity properties of functional equations in several variables.
• Une remarque sur les équations fonctionnelles
• Cauchy functional equation and generalized continuity
• A Micronote on a Functional Equation
• Connected and disconnected plane sets and the functional equation 𝑓(𝑥)+𝑓(𝑦)=𝑓(𝑥+𝑦)

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