Explicit stochastic analysis of Brownian motion and point measures on Riemannian manifolds
The authors study the three types of gradient operators of stochastic analysis on Riemannian manifolds in the Gaussian measure setting [see also \textit{S. Fang} and \textit{P. Malliavin}, J. Funct. Anal. 118, No. 1, 249-274 (1993; Zbl 0798.58080)] and in the Poisson measure setting. They obtain explicit formulas linking the gradients by explicit calculations using the Fock gradient and divergence of the flat case. Their method shows that the difficulties of stochastic calculus on manifolds are similar to those of the Poisson case. The anticipating integral on manifolds is also treated [see also \textit{S. Fang}, J. Funct. Anal. 131, No. 1, 228-253 (1995; Zbl 0847.58081)].
scientific article; zbMATH DE number 1346907