The aims of this book, originally published in 1982, are to give an
understanding of the basic ideas concerning stochastic differential
equations on manifolds and their solution flows, to examine the
properties of Brownian motion on Riemannian manifolds when it is
constructed using the stochiastic development and to indicate some
of the uses of the theory. The author has included two appendices
which summarise the manifold theory and differential geometry
needed to follow the development; coordinate-free notation is used
throughout. Moreover, the stochiastic integrals used are those
which can be obtained from limits of the Riemann sums, thereby
avoiding much of the technicalities of the general theory of
processes and allowing the reader to get a quick grasp of the
fundamental ideas of stochastic integration as they are needed for
a variety of applications.
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