After an extensive unsuccessful search: I need a reference (preferably a book) for the Donsker's invariance principle for Riemannian manifolds. Thanks.



Reference needed: Donsker's Invariance Principle for Riemannian Manifolds
The generalization of Donsker's theorem from $N$-dimensional Euclidean space to general Riemannian manifolds has been worked out by Erik Jørgensen, [The Central Limit Problem for Geodesic Random Walks](http://link.springer.com/content/pdf/10.1007%2FBF00533088).



> 
> The purpose of the present work is to
>  consider the problem of defining the
>  concept of a random walk in a general
>  Riemannian manifold ${\cal M}$, and to
>  investigate the behavior in the limit
>  of a sequence of such random walks. It
>  will be shown that such a sequence,
>  under reasonable assumptions,
>  converges to a diffusion process in
>  ${\cal M}$, and in particular Brownian motion
>  processes will be obtained as limits
>  of sequences of random walks with
>  identically distributed steps. The
>  results which we arrive at in this
>  paper are general versions of
>  well-known classical results
>  concerning the transition from random
>  walks to diffusion processes, for
>  instance: the central limit theorem
>  and Donsker's theorem.
> 
> 
> 


