Martingale Transformations of Brownian Motion with Application to Functional Equations

2021/08/15 by Michael Mania, Mania, M., Revaz Tevzadze +1
Mathematics · #60G44 #60J65 #97I70 #FOS: Mathematics #Functional Equations Stability Results #Mathematical Dynamics and Fractals #Nonlinear Differential Equations Analysis #Probability (math.PR)

paper · pdf · doi:10.48550/arxiv.2108.06694

openalex publication_date 2021/08/15 · openalex created_date 2021/08/30 · openalex updated_date 2026/07/28

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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