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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.

MSC:

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