## The Annals of Probability

### Harmonic coordinates for diffusions in the plane

G. Kersting

#### 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.

#### Article information

Source
Ann. Probab., Volume 24, Number 3 (1996), 1239-1268.

Dates
First available in Project Euclid: 9 October 2003

https://projecteuclid.org/euclid.aop/1065725180

Digital Object Identifier
doi:10.1214/aop/1065725180

Mathematical Reviews number (MathSciNet)
MR1411493

Zentralblatt MATH identifier
0868.60063

Subjects
Primary: 60J60
Secondary: 60H30: Applications of stochastic analysis (to PDE, etc.) 57R50: Diffeomorphisms 58G32

#### Citation

Kersting, G. Harmonic coordinates for diffusions in the plane. Ann. Probab. 24 (1996), no. 3, 1239--1268. doi:10.1214/aop/1065725180. https://projecteuclid.org/euclid.aop/1065725180