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.
Publié le : 1996-07-14
Classification:
Diffusion processes,
dynamical systems,
harmonic mappings,
harmonic coordinates,
coupling methods,
Poisson equation in unbounded domains,
a priori estimates,
60J60,
60H30,
57R50,
58G32
@article{1065725180,
author = {Kersting, G.},
title = {Harmonic coordinates for diffusions in the plane},
journal = {Ann. Probab.},
volume = {24},
number = {2},
year = {1996},
pages = { 1239-1268},
language = {en},
url = {http://dml.mathdoc.fr/item/1065725180}
}
Kersting, G. Harmonic coordinates for diffusions in the plane. Ann. Probab., Tome 24 (1996) no. 2, pp. 1239-1268. http://gdmltest.u-ga.fr/item/1065725180/