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arXiv · 2108.06694

Martingale Transformations of Brownian Motion with Application to Functional Equations

M. Mania·R. Tevzadze
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Abstract

We describe the classes of functions $f=(f(x), x\in R)$, 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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M. Mania, R. Tevzadze. 2021-08-15. Martingale Transformations of Brownian Motion with Application to Functional Equations. https://arxiv.org/abs/2108.06694

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