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001 978-3-540-47022-9
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008 121227s1999 gw | s |||| 0|eng d
020 _a9783540470229
_9978-3-540-47022-9
024 7 _a10.1007/BFb0103064
_2doi
050 4 _aQA273.A1-274.9
050 4 _aQA274-274.9
072 7 _aPBT
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072 7 _aMAT029000
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_2thema
072 7 _aPBWL
_2thema
082 0 4 _a519.2
_223
100 1 _aElworthy, K. David.
_eauthor.
_4aut
_4http://id.loc.gov/vocabulary/relators/aut
245 1 0 _aOn the Geometry of Diffusion Operators and Stochastic Flows
_h[electronic resource] /
_cby K. David Elworthy, Yves Le Jan, Xue-Mei Li.
264 1 _aBerlin, Heidelberg :
_bSpringer Berlin Heidelberg :
_bImprint: Springer,
_c1999.
300 _aV, 105 p.
_bonline resource.
336 _atext
_btxt
_2rdacontent
337 _acomputer
_bc
_2rdamedia
338 _aonline resource
_bcr
_2rdacarrier
347 _atext file
_bPDF
_2rda
490 1 _aLecture Notes in Mathematics,
_x0075-8434 ;
_v1720
505 0 _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.
520 _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.
650 0 _aDistribution (Probability theory.
650 0 _aFunctional analysis.
650 0 _aGlobal differential geometry.
650 0 _aGlobal analysis.
650 1 4 _aProbability Theory and Stochastic Processes.
_0http://scigraph.springernature.com/things/product-market-codes/M27004
650 2 4 _aFunctional Analysis.
_0http://scigraph.springernature.com/things/product-market-codes/M12066
650 2 4 _aDifferential Geometry.
_0http://scigraph.springernature.com/things/product-market-codes/M21022
650 2 4 _aGlobal Analysis and Analysis on Manifolds.
_0http://scigraph.springernature.com/things/product-market-codes/M12082
700 1 _aJan, Yves Le.
_eauthor.
_4aut
_4http://id.loc.gov/vocabulary/relators/aut
700 1 _aLi, Xue-Mei.
_eauthor.
_4aut
_4http://id.loc.gov/vocabulary/relators/aut
710 2 _aSpringerLink (Online service)
773 0 _tSpringer eBooks
776 0 8 _iPrinted edition:
_z9783540667087
776 0 8 _iPrinted edition:
_z9783662203460
830 0 _aLecture Notes in Mathematics,
_x0075-8434 ;
_v1720
856 4 0 _uhttps://doi.org/10.1007/BFb0103064
912 _aZDB-2-SMA
912 _aZDB-2-LNM
912 _aZDB-2-BAE
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