LEADER 03636nam 22008295 450 001 9910146313003321 005 20250730104802.0 010 $a3-540-47022-0 024 7 $a10.1007/BFb0103064 035 $a(CKB)1000000000437293 035 $a(SSID)ssj0000325366 035 $a(PQKBManifestationID)12116393 035 $a(PQKBTitleCode)TC0000325366 035 $a(PQKBWorkID)10321709 035 $a(PQKB)11050538 035 $a(DE-He213)978-3-540-47022-9 035 $a(MiAaPQ)EBC5610669 035 $a(Au-PeEL)EBL5610669 035 $a(OCoLC)1078995943 035 $a(MiAaPQ)EBC6812146 035 $a(Au-PeEL)EBL6812146 035 $a(OCoLC)1287131741 035 $a(PPN)155177729 035 $a(EXLCZ)991000000000437293 100 $a20121227d1999 u| 0 101 0 $aeng 135 $aurnn#008mamaa 181 $ctxt 182 $cc 183 $acr 200 10$aOn the Geometry of Diffusion Operators and Stochastic Flows /$fby K.D. Elworthy, Y. Le Jan, Xue-Mei Li 205 $a1st ed. 1999. 210 1$aBerlin, Heidelberg :$cSpringer Berlin Heidelberg :$cImprint: Springer,$d1999. 215 $a1 online resource (V, 105 p.) 225 1 $aLecture Notes in Mathematics,$x1617-9692 ;$v1720 300 $aBibliographic Level Mode of Issuance: Monograph 311 08$a3-540-66708-3 327 $aConstruction 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. 330 $aStochastic differential equations, and Hoermander form representations of diffusion operators, can determine a linear connection associated to the underlying (sub)-Riemannian structure. This is systematically described, together with its invariants, and then exploited to discuss qualitative properties of stochastic flows, and analysis on path spaces of compact manifolds with diffusion measures. This should be useful to stochastic analysts, especially those with interests in stochastic flows, infinite dimensional analysis, or geometric analysis, and also to researchers in sub-Riemannian geometry. A basic background in differential geometry is assumed, but the construction of the connections is very direct and itself gives an intuitive and concrete introduction. Knowledge of stochastic analysis is also assumed for later chapters. 410 0$aLecture Notes in Mathematics,$x1617-9692 ;$v1720 606 $aProbabilities 606 $aFunctional analysis 606 $aGeometry, Differential 606 $aGlobal analysis (Mathematics) 606 $aManifolds (Mathematics) 606 $aProbability Theory 606 $aFunctional Analysis 606 $aDifferential Geometry 606 $aGlobal Analysis and Analysis on Manifolds 615 0$aProbabilities. 615 0$aFunctional analysis. 615 0$aGeometry, Differential. 615 0$aGlobal analysis (Mathematics) 615 0$aManifolds (Mathematics) 615 14$aProbability Theory. 615 24$aFunctional Analysis. 615 24$aDifferential Geometry. 615 24$aGlobal Analysis and Analysis on Manifolds. 676 $a519.233 686 $a58G32$2msc 686 $a53B05$2msc 686 $a60H10$2msc 700 $aElworthy$b K. D.$050902 702 $aLe Jan$b Y.$f1952- 702 $aLi$b X-M.$f1964- 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910146313003321 996 $aGeometry of diffusion operators and stochastic flows$9374265 997 $aUNINA