arXiv Analytics

Sign in

arXiv:1307.3155 [math.PR]AbstractReferencesReviewsResources

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

Michael R. Tehranchi

Published 2013-07-11, updated 2015-07-01Version 2

It is shown that if the processes $B$ and $f(B)$ are both Brownian motions 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.

Comments: 4 pages
Categories: math.PR
Subjects: 60H30, 35C05
Related articles: Most relevant | Search more
arXiv:math/0611292 [math.PR] (Published 2006-11-09, updated 2009-08-26)
Consistent families of Brownian motions and stochastic flows of kernels
arXiv:1703.07234 [math.PR] (Published 2017-03-21)
Convergence of Brownian Motions on Metric Measure Spaces Under Riemannian Curvature-Dimension Conditions
arXiv:1102.4533 [math.PR] (Published 2011-02-22)
Construction of the Paths of Brownian Motions on Star Graphs

Links

Toolbox