Abstract
For a class of diffusions X in the plane we construct a global system of coordinates $u(x)$, such that $u(x)$ is close to X at infinity and $u(X)$ is a local martingale. Such coordinates are useful for the study of the long term behaviour of X. The construction uses probabilistic methods, in particular a coupling for general diffusions in the plane.
Citation
G. Kersting. "Harmonic coordinates for diffusions in the plane." Ann. Probab. 24 (3) 1239 - 1268, July 1996. https://doi.org/10.1214/aop/1065725180
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