Abstract:We describe the classes of functions f = (f (x), x ∈ R), for which processes f (W t ) − Ef (W t ) and f (W t )/Ef (W t ) 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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