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What is an analogous version of the Ornstein–Uhlenbeck process on Riemannian manifolds?
Recall that the Ornstein–Uhlenbeck (OU) process in $\mathbb{R}^d$ is defined by the following SDE,
$$
d Z_t=\frac{-1}{2} Z_t d t+d W_t, \quad t \geqslant 0
$$
where $\left(W_t\right)_{t \geqslant 0}$ ...
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