On the Geometry of Diffusion Operators and Stochastic Flows. Lecture Notes in Mathematics, Band 1720

Seitenzahl:

118

Gewicht:

176 g

Erschienen bei:

Springer

Kurzbeschreibung

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. TOC: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.

Mehr über...

Mehr über:  Stochastik, Riemannsche Geometrie, Diffusionsoperator, Stochastische Differenzialgleichungen, Stochastische Flüsse, Differentialoperator, connections, Stochastic differential equations, differential forms, path space, sub-Riemannian geometry

Mehr von: 

Mehr von:  Y. Le Jan, K. D. Elworthy, Xue-Mei Li, Springer-Verlag GmbH