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arXiv · 1307.3155

If $B$ and $f(B)$ are Brownian motions, then $f$ is affine

Michael R. Tehranchi
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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.

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Michael R. Tehranchi. 2013-07-11. If $B$ and $f(B)$ are Brownian motions, then $f$ is affine. https://doi.org/10.1216/rmj-2017-47-3-947

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