Functional equations and martingales

We consider functional equations (Cauchy’s, Abel’s and some other functional equations) and show that finding the general solution of these equations is equivalent to establishing that a space-transformation of a Brownian Motion by a suitable function (or functions) is a martingale.

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Bibliographic Details
Published inAequationes mathematicae Vol. 96; no. 1; pp. 221 - 241
Main Authors Mania, M., Tikanadze, L.
Format Journal Article
LanguageEnglish
Published Cham Springer International Publishing 01.02.2022
Springer Nature B.V
Subjects
Analysis
Brownian motion
Combinatorics
Functional equations
Martingales
Mathematical analysis
Mathematics
Mathematics and Statistics
Theorems
60J65
97I70
60G44
Functional equations
Brownian Motion
Martingales
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Summary:We consider functional equations (Cauchy’s, Abel’s and some other functional equations) and show that finding the general solution of these equations is equivalent to establishing that a space-transformation of a Brownian Motion by a suitable function (or functions) is a martingale.
ISSN:0001-9054
1420-8903
DOI:10.1007/s00010-021-00807-9