Stochastic Differential Equations on Manifolds

by K. D. Elworthy

Overview

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.

Product Details

ISBN-13:	9780521287678
Publisher:	Cambridge University Press
Publication date:	09/02/1982
Series:	London Mathematical Society Lecture Note Series , #70
Pages:	348
Product dimensions:	5.98(w) x 9.02(h) x 0.79(d)

Table of Contents

Preface; Introduction; 1. Preliminaries and notation; 2. Kolmogorov's Theorem, Totoki's Theorem, and Brownian Motion; 3. The integral: estimates and existence; 4. Special cases; 5. The change of variable formula; 6. Stochastic integral equations; 7. Stochastic differential equations on manifolds; 8. Regularity; 9. Diffusions; Appendices; References; Index.