On Martingale Transformations of Multidimensional Brownian Motion
Michael Mania, Revaz Tevzadze
TL;DR
This paper characterizes functions transforming multidimensional Brownian motion into martingales and applies this to solve the multidimensional Cauchy functional equation.
Contribution
It provides a comprehensive description of functions that turn vector Brownian motion into martingales and links this to solutions of the Cauchy functional equation.
Findings
Characterization of functions transforming Brownian motion into martingales
Martingale-based solution of the multidimensional Cauchy functional equation
New insights into the structure of measurable solutions
Abstract
We describe the class of functions which transform a vector Brownian Motion into a martingale and use this description to give martingale characterization of the general measurable solution of the multidimensional Cauchy functional equation.
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