The radial part of Brownian motion on a manifold: A semimartingale property
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.
scientific article; zbMATH DE number 4056729