ENGLISH

On the Geometry of Diffusion Operators and Stochastic Flows

By K. David Elworthy , Yves Le Jan , Xue-Mei Li (auth.)

Book information

Publisher
Springer-Verlag Berlin Heidelberg
Year
1999
ISBN
978-3-540-66708-7, 978-3-540-47022-9
DOI
10.1007/BFb0103064
Language
english
Format
PDF
Filesize
2 MB (1662468 bytes)
Series
Lecture Notes in Mathematics 1720
Edition
1
Pages
105\120
Orientation
yes
Scanned
yes
Time added
2013-08-01 04:00:00
Probability Theory and Stochastic Processes; Globa

Description

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.

Similar books