Continuous extensions of skew product diffusions
type: Item
instance of: scholarly article
title: Continuous extensions of skew product diffusions
zbMATH Open document ID: 0696.60075
DOI: 10.1007/BF01377630
author: K. Bruce Erickson
publication date: 1990-01-01T00:00:00Z
review text: 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.
Mathematics Subject Classification ID: 60J60
zbMATH DE Number: 4140966
zbMATH Keywords: skew product diffusion
zbMATH Keywords: additive functional
zbMATH Keywords: strong Markov property
MaRDI profile type: Publication
cites work: Q5556844
cites work: Q5332526
cites work: Renaissance, recollements, mélanges, ralentissement de processus de Markov
cites work: Q4187050
published in: Zeitschrift für Wahrscheinlichkeitstheorie und Verwandte Gebiete
description: scientific article; zbMATH DE number 4140966