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Stochastic Differential Equations on Manifolds : Themes in the Social Sciences - K. D. Elworthy

Stochastic Differential Equations on Manifolds

Themes in the Social Sciences

Paperback

Published: 1st November 1982
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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.

Preface
Introduction
Preliminaries and notation
Kolmogorov's Theorem, Totoki's Theorem, and Brownian Motion
The integral: estimates and existence
Special Cases
The change of variable formula
Stochastic integral equations
Stochastic differential equations on manifolds
Regularity
Diffusions
Appendices
References
Index
Table of Contents provided by Publisher. All Rights Reserved.

ISBN: 9780521287678
ISBN-10: 0521287677
Series: Themes in the Social Sciences
Audience: Tertiary; University or College
Format: Paperback
Language: English
Number Of Pages: 348
Published: 1st November 1982
Publisher: CAMBRIDGE UNIV PR
Country of Publication: GB
Dimensions (cm): 22.86 x 15.24  x 1.98
Weight (kg): 0.51