03152nam 2200697 450 99646665080331620220818142703.03-540-47022-010.1007/BFb0103064(CKB)1000000000437293(SSID)ssj0000325366(PQKBManifestationID)12116393(PQKBTitleCode)TC0000325366(PQKBWorkID)10321709(PQKB)11050538(DE-He213)978-3-540-47022-9(MiAaPQ)EBC5610669(Au-PeEL)EBL5610669(OCoLC)1078995943(MiAaPQ)EBC6812146(Au-PeEL)EBL6812146(OCoLC)1287131741(PPN)155177729(EXLCZ)99100000000043729320220818d1999 uy 0engurnn#008mamaatxtccrOn the geometry of diffusion operators and stochastic flows /K.D. Elworthy, Y. Le Jan, Xue-Mei Li1st ed. 1999.Berlin :Springer,[1999]©19991 online resource (V, 105 p.)Lecture notes in mathematics (Springer-Verlag) ;1720Bibliographic Level Mode of Issuance: Monograph3-540-66708-3 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.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.Lecture notes in mathematics (Springer-Verlag) ;1720.Diffusion processesLinear operatorsFlows (Differentiable dynamical systems)Diffusion processes.Linear operators.Flows (Differentiable dynamical systems)519.23358G32msc53B05msc60H10mscElworthy K. D.50902Le Jan Y.1952-Li X-M.1964-MiAaPQMiAaPQMiAaPQBOOK996466650803316Geometry of diffusion operators and stochastic flows374265UNISA