# Mean Derivatives on Manifolds

Chapter

## Abstract

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.

## Keywords

Weak Solution Riemannian Manifold Probability Space Covariant Derivative Current Velocity
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## Copyright information

© Springer-Verlag London Limited 2011