The radial part of Brownian motion on a manifold: A semimartingale property
type: Item
instance of: scholarly article
title: The radial part of Brownian motion on a manifold: A semimartingale property
zbMATH Open document ID: 0647.60086
author: Wilfrid S. Kendall
published in: The Annals of Probability
publication date: 1987-01-01T00:00:00Z
review text: Let M be a complete Riemannian manifold, r(x) a distance in M of x from a fixed point p, and \(X=X_ t\) a Brownian motion on M. For many manifolds M, r(\(\cdot)\) is not smooth and that is why Itô's formula can't be applied to r(X) as usual. The author proved that r(X) is a semimartingale and obtained its decomposition into the sum of a local martingale and an increasing process. The explicit form of the local martingale part is given.
Mathematics Subject Classification ID: 60J65
Mathematics Subject Classification ID: 58J65
zbMATH DE Number: 4056729
zbMATH Keywords: Riemannian manifold
zbMATH Keywords: Itô's formula
zbMATH Keywords: semimartingale
zbMATH Keywords: decomposition
zbMATH Keywords: local martingale
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1214/aop/1176991988
OpenAlex ID: W2090041803
DOI: 10.1214/AOP/1176991988
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description: scientific article; zbMATH DE number 4056729