Mean Derivatives on Manifolds
Let a connection H be given on a manifold M. Let ξ(t) be a stochastic process on M. According to formulae (8.1) and (8.2) we can introduce mean forward and mean backward derivatives of ξ(t), if they exist, in any chart. However, from formula (7.19) it follows that for solutions of (7.18) we would obtain the mean derivatives depending on the local connector of the connection H in the chart and even on A, while for physical reasons the derivatives should be vectors. This is why we modify the definition of mean derivatives as follows.
KeywordsWeak Solution Riemannian Manifold Probability Space Covariant Derivative Current Velocity
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