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Stochastic Differential Equations on Manifolds is written by K. D. Elworthy and published by Cambridge University Press. It's available with International Standard Book Number or ISBN identification 0521287677 (ISBN 10) and 9780521287678 (ISBN 13).
A basic 1982 treatment of stochastic differential equations on manifolds and their solution flows and the properties of Brownian motion on Riemannian manifolds.