Continuous extensions of skew product diffusions
A skew product diffusion in \(R^ d\) which hits the origin and is killed there has a unique continuous extension (a conservative diffusion process without sojourn at 0) if and only if it spins around the origin infinitely often as it approaches and hits the origin. Otherwise there are infinitely many distinct continuous extensions and these are in a one-to-one correspondence with the set of probability measures on the unit sphere. This correspondence is given an explicit and intuitive description. A skew product diffusion is a strong Markov process with continuous paths for which the radial part is a diffusion process on the positive real line and the spherical projection is an independent diffusion run with an additive functional of the radial process. This description of the skew product process can only be valid up to the hitting time at the origin at which time the strong Markov property breaks down.
scientific article; zbMATH DE number 4140966