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000696020 020__ $$a9783319002279 $$qelectronic book
000696020 020__ $$a3319002279 $$qelectronic book
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000696020 0247_ $$a10.1007/978-3-319-00227-9$$2doi
000696020 035__ $$aSP(OCoLC)ocn863638322
000696020 035__ $$aSP(OCoLC)863638322
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000696020 08204 $$a519.2/33$$223
000696020 1001_ $$aBakry, D.$$q(Dominique),$$eauthor.
000696020 24510 $$aAnalysis and geometry of Markov diffusion operators$$h[electronic resource]  /$$cDominique Bakry, Ivan Gentil, Michel Ledoux.
000696020 264_1 $$aCham :$$bSpringer,$$c2014.
000696020 300__ $$a1 online resource (xx, 552 pages).
000696020 336__ $$atext$$btxt$$2rdacontent
000696020 337__ $$acomputer$$bc$$2rdamedia
000696020 338__ $$aonline resource$$bcr$$2rdacarrier
000696020 4901_ $$aGrundlehren der mathematischen Wissenschaften ;$$v348
000696020 504__ $$aIncludes bibliographical references and index.
000696020 5050_ $$aIntroduction -- Part I Markov semigroups, basics and examples: 1.Markov semigroups -- 2.Model examples -- 3.General setting -- Part II Three model functional inequalities: 4.Poincar inequalities -- 5.Logarithmic Sobolev inequalities -- 6.Sobolev inequalities -- Part III Related functional, isoperimetric and transportation inequalities: 7.Generalized functional inequalities -- 8.Capacity and isoperimetry-type inequalities -- 9.Optimal transportation and functional inequalities -- Part IV Appendices: A.Semigroups of bounded operators on a Banach space -- B.Elements of stochastic calculus -- C.Some basic notions in differential and Riemannian geometry -- Notations and list of symbols.
000696020 506__ $$aAccess limited to authorized users.
000696020 520__ $$aThe present volume is an extensive monograph on the analytic and geometric aspects of Markov diffusion operators. It focuses on the geometric curvature properties of the underlying structure in order to study convergence to equilibrium, spectral bounds, functional inequalities such as Poincar, Sobolev or logarithmic Sobolev inequalities, and various bounds on solutions of evolution equations. At the same time, it covers a large class of evolution and partial differential equations. The book is intended to serve as an introduction to the subject and to be accessible for beginning and advanced scientists and non-specialists. Simultaneously, it covers a wide range of results and techniques from the early developments in the mid-eighties to the latest achievements. As such, students and researchers interested in the modern aspects of Markov diffusion operators and semigroups and their connections to analytic functional inequalities, probabilistic convergence to equilibrium and geometric curvature will find it especially useful. Selected chapters can also be used for advanced courses on the topic.
000696020 588__ $$aDescription based on print version record.
000696020 650_0 $$aMarkov operators.
000696020 7001_ $$aGentil, Ivan,$$eauthor.
000696020 7001_ $$aLedoux, Michel,$$d1958-,$$eauthor.
000696020 77608 $$iPrint version:$$aBakry, D. (Dominique), author.$$tAnalysis and geometry of Markov diffusion operators$$z3319002260$$w(OCoLC)860706678
000696020 830_0 $$aGrundlehren der mathematischen Wissenschaften ;$$v348.
000696020 85280 $$bebk$$hSpringerLink
000696020 85640 $$3SpringerLink$$uhttps://univsouthin.idm.oclc.org/login?url=http://dx.doi.org/10.1007/978-3-319-00227-9$$zOnline Access
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000696020 980__ $$aEBOOK
000696020 980__ $$aBIB
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