Functional equations and martingales

2019/12/13 by Mania, Michael, Tikanadze, Luka
#FOS: Mathematics #Probability (math.PR)

paper · doi:10.48550/arxiv.1912.06299

Abstract

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

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• On Martingale Transformations of Multidimensional Brownian Motion
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• Functional Equations for the Stochastic Exponential
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