Conditional mathematical expectation and martingales on a smooth manifold. (Russian. English summary) Zbl 0664.60017

The conditional expectation on a smooth Riemannian manifold is defined as a random variable which minimizes the quadratic functional. Some properties and applications for the definition of martingales are considered.


60B99 Probability theory on algebraic and topological structures
58J65 Diffusion processes and stochastic analysis on manifolds
60G44 Martingales with continuous parameter