Dirichlet forms,quasiregular functions and Brownian motion

Summary Given a quasiregular function on an open setU in ⁿ it is shown that there exists a diffusionX _t inU such that mapsX _t inton-dimensional Brownian motion. The process is constructed from a Dirichlet form which can be described explicitly. This enables us to apply stochastic methods in the investigation of quasiregular mappings. Some examples of applications are given, including boundary behaviour and value distribution.