On the Geometry of Diffusion Operators and Stochastic Flows

  • Authors
  • K. David Elworthy
  • Yves Le Jan
  • Xue-Mei Li

Part of the Lecture Notes in Mathematics book series (LNM, volume 1720)

Table of contents

  1. Front Matter
    Pages I-2
  2. K. D. Elworthy, J. Le Jan, Xue-Mei Li
    Pages 3-6
  3. K. David Elworthy, Yves Le Jan, Xue-Mei Li
    Pages 7-29
  4. K. David Elworthy, Yves Le Jan, Xue-Mei Li
    Pages 30-56
  5. K. David Elworthy, Yves Le Jan, Xue-Mei Li
    Pages 57-75
  6. K. David Elworthy, Yves Le Jan, Xue-Mei Li
    Pages 76-86
  7. K. David Elworthy, Yves Le Jan, Xue-Mei Li
    Pages 87-94
  8. K. David Elworthy, Yves Le Jan, Xue-Mei Li
    Pages 95-110
  9. Back Matter
    Pages 111-116

About this book

Introduction

Stochastic differential equations, and Hoermander form representations of diffusion operators, can determine a linear connection associated to the underlying (sub)-Riemannian structure. This is systematically described, together with its invariants, and then exploited to discuss qualitative properties of stochastic flows, and analysis on path spaces of compact manifolds with diffusion measures. This should be useful to stochastic analysts, especially those with interests in stochastic flows, infinite dimensional analysis, or geometric analysis, and also to researchers in sub-Riemannian geometry. A basic background in differential geometry is assumed, but the construction of the connections is very direct and itself gives an intuitive and concrete introduction. Knowledge of stochastic analysis is also assumed for later chapters.

Keywords

Measure Riemannian geometry Stochastic differential equations connections differential forms differential geometry manifold path space sub-Riemannian geometry

Bibliographic information

  • DOI https://doi.org/10.1007/BFb0103064
  • Copyright Information Springer-Verlag Berlin Heidelberg 1999
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Springer Book Archive
  • Print ISBN 978-3-540-66708-7
  • Online ISBN 978-3-540-47022-9
  • Series Print ISSN 0075-8434
  • Series Online ISSN 1617-9692
  • About this book