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- catalog abstract "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.".
- catalog contributor b11529903.
- catalog contributor b11529904.
- catalog contributor b11529905.
- catalog created "1999.".
- catalog date "1999".
- catalog date "1999.".
- catalog dateCopyrighted "1999.".
- catalog description "Construction of connections -- The infinitesimal generators and associated operators -- Decomposition of noise and Itering -- Application: Analysis on spaces of paths -- Stability of stochastic dynamical systems -- Appendices.".
- catalog 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.".
- catalog extent "118 p. ;".
- catalog identifier "3540667083 (softcover : alk. paper)".
- catalog isPartOf "Lecture notes in mathematics (Springer-Verlag) ; 1720.".
- catalog isPartOf "Lecture notes in mathematics, 0075-8434 ; 1720".
- catalog issued "1999".
- catalog issued "1999.".
- catalog language "eng".
- catalog publisher "New York : Springer,".
- catalog subject "510 s 519.2/33 21".
- catalog subject "Diffusion processes.".
- catalog subject "Distribution (Probability theory).".
- catalog subject "Flows (Differentiable dynamical systems)".
- catalog subject "Global analysis (Mathematics)".
- catalog subject "Global differential geometry.".
- catalog subject "Linear operators.".
- catalog subject "Mathematics.".
- catalog subject "QA3.L28 no. 1720 QA274.75".
- catalog tableOfContents "Construction of connections -- The infinitesimal generators and associated operators -- Decomposition of noise and Itering -- Application: Analysis on spaces of paths -- Stability of stochastic dynamical systems -- Appendices.".
- catalog title "On the geometry of diffusion operators and stochastic flows / D. Elworthy, Y. Le Jan, X-M. Li.".
- catalog type "text".