Stochastic anticipative calculus on the path space over a compact Riemannian manifold
The author considers a Riemannian path space; the divergence operator on this space can be considered as an anticipative integral on the Riemannian manifold. The aim of this work is to extend some results which were previously known for Euclidean space; the difficulty comes from the fact that Lie brackets of vector fields are no more vector fields. Nevertheless, the author obtains an Itô formula and a maximal inequality for these anticipative integrals.
scientific article; zbMATH DE number 1187610