1.

Record Nr.

UNINA9910146313003321

Autore

Elworthy K. D.

Titolo

On the Geometry of Diffusion Operators and Stochastic Flows / / by K.D. Elworthy, Y. Le Jan, Xue-Mei Li

Pubbl/distr/stampa

Berlin, Heidelberg : , : Springer Berlin Heidelberg : , : Imprint : Springer, , 1999

ISBN

3-540-47022-0

Edizione

[1st ed. 1999.]

Descrizione fisica

1 online resource (V, 105 p.)

Collana

Lecture Notes in Mathematics, , 1617-9692 ; ; 1720

Classificazione

58G32

53B05

60H10

Disciplina

519.233

Soggetti

Probabilities

Functional analysis

Geometry, Differential

Global analysis (Mathematics)

Manifolds (Mathematics)

Probability Theory

Functional Analysis

Differential Geometry

Global Analysis and Analysis on Manifolds

Lingua di pubblicazione

Inglese

Formato

Materiale a stampa

Livello bibliografico

Monografia

Note generali

Bibliographic Level Mode of Issuance: Monograph

Nota di contenuto

Construction of connections -- The infinitesimal generators and associated operators -- Decomposition of noise and filtering -- Application: Analysis on spaces of paths -- Stability of stochastic dynamical systems -- Appendices.

Sommario/riassunto

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.