Barycenters and martingales on a manifold. (Barycentres et martingales sur une variété.) (French) Zbl 0817.58047

Picard, Jean

Ann. Inst. Henri Poincaré, Probab. Stat. 30, No. 4, 647-702 (1994).

Author’s abstract: “On a manifold \(V\), we consider a family of \(V\)- valued maps, called barycentres, defined on the set of probability measures on \(V\). For each barycentre we define the class of martingales on \(V\) as the set of \(V\)-valued semimartingales with jumps which satisfy a condition involving the barycentre; this notion extends the notion of continuous martingales defined by means of the second order differential geometry. We give several equivalent characterizations and prove that under assumptions, there exists one and only one martingale with prescribed final value”.

Reviewer: S.Eloshvili (Tbilisi)

MSC:

58J65	Diffusion processes and stochastic analysis on manifolds
60G48	Generalizations of martingales

Keywords:

Riemannian manifold; semimartingale; barycentres; martingales