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2017 If $B$ and $f(B)$ are Brownian motions, then $f$ is affine
Michael R. Tehranchi
Rocky Mountain J. Math. 47(3): 947-953 (2017). DOI: 10.1216/RMJ-2017-47-3-947

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. "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

Information

Published: 2017
First available in Project Euclid: 24 June 2017

zbMATH: 1369.31011
MathSciNet: MR3682156
Digital Object Identifier: 10.1216/RMJ-2017-47-3-947

Subjects:
Primary: 31B05, 35Q60, 60J65

Rights: Copyright © 2017 Rocky Mountain Mathematics Consortium

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Vol.47 • No. 3 • 2017
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