A probabilistic method of solving Lobachevsky's functional equation.

The aim of this paper is to give a probabilistic (martingale) characterization to the general measurable solution of the Lobachevsky functional equation. We show that finding the general solution of this equation is equivalent to establishing that a space-transformation of a Brownian Motion by a suitable function is a martingale. This method can be applied for Cauchy's, Jensen's and some other functional equations. [ABSTRACT FROM AUTHOR]