Lecture Notes in Mathematics

On the Geometry of Diffusion Operators and Stochastic Flows

Authors: Elworthy, K.D., Le Jan, Y., Li, Xue-Mei

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About this book

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.

Table of contents (7 chapters)

  • Introduction

    Elworthy, K. D. (et al.)

    Pages 3-6

  • Construction of connections

    Elworthy, K. David (et al.)

    Pages 7-29

  • The infinitesimal generators and associated operators

    Elworthy, K. David (et al.)

    Pages 30-56

  • Decomposition of noise and filtering

    Elworthy, K. David (et al.)

    Pages 57-75

  • Application: Analysis on spaces of paths

    Elworthy, K. David (et al.)

    Pages 76-86

Buy this book

eBook $29.99
price for USA (gross)
  • ISBN 978-3-540-47022-9
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Softcover $39.95
price for USA
  • ISBN 978-3-540-66708-7
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
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Bibliographic Information

Bibliographic Information
Book Title
On the Geometry of Diffusion Operators and Stochastic Flows
Authors
Series Title
Lecture Notes in Mathematics
Series Volume
1720
Copyright
1999
Publisher
Springer-Verlag Berlin Heidelberg
Copyright Holder
Springer-Verlag Berlin Heidelberg
eBook ISBN
978-3-540-47022-9
DOI
10.1007/BFb0103064
Softcover ISBN
978-3-540-66708-7
Series ISSN
0075-8434
Edition Number
1
Number of Pages
V, 105
Topics