Addressed to both pure and applied probabilitists, including graduate
students, this text is a pedagogically-oriented introduction to the
Schwartz-Meyer second-order geometry and its use in stochastic calculus.
P.A. Meyer has contributed an appendix: "A short presentation of
stochastic calculus" presenting the basis of stochastic calculus and
thus making the book better accessible to non-probabilitists also. No
prior knowledge of differential geometry is assumed of the reader: this
is covered within the text to the extent. The general theory is
presented only towards the end of the book, after the reader has been
exposed to two particular instances - martingales and Brownian motions -
in manifolds. The book also includes new material on non-confluence of
martingales, s.d.e. from one manifold to another, approximation results
for martingales, solutions to Stratonovich differential equations. Thus
this book will prove very useful to specialists and non-specialists
alike, as a self-contained introductory text or as a compact reference.