Abstract
It is shown that, if the processes $B$ and $f(B)$ are both Brownian motions (without a random time change), then $f$ must be an affine function. As a by-product of the proof it is shown that the only functions which are solutions to both the Laplace equation and the eikonal equation are affine.
Citation
Michael R. Tehranchi. "If $B$ and $f(B)$ are Brownian motions, then $f$ is affine." Rocky Mountain J. Math. 47 (3) 947 - 953, 2017. https://doi.org/10.1216/RMJ-2017-47-3-947
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