Martingale Transformations of Brownian Motion with Application to Functional Equations
Abstract
We describe the classes of functions f=(f(x), x∈ R), for which processes f(Wt)-Ef(Wt) and f(Wt)/Ef(Wt) are martingales. We apply these results to give a martingale characterization of general solutions of the quadratic and the D'Alembert functional equations. We study also the time-dependent martingale transformations of a Brownian Motion.
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