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Analysis and geometry of Markov diff...

Bakry, D.

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Analysis and geometry of Markov diffusion operators /

紀錄類型:	書目-語言資料,印刷品 : Monograph/item
正題名/作者:	Analysis and geometry of Markov diffusion operators // by Dominique Bakry, Ivan Gentil, Michel Ledoux.
作者:	Bakry, D.
其他作者:	Gentil, Ivan.
出版者:	Cham :Springer, : 2014.,
面頁冊數:	xx, 552 p. :ill ;24 cm.
標題:	Markov processes. -
ISBN:	9783319002262 (hbk.) :
ISSN:	00727830

Analysis and geometry of Markov diffusion operators /
Bakry, D.

Analysis and geometry of Markov diffusion operators /by Dominique Bakry, Ivan Gentil, Michel Ledoux. - Cham :Springer,2014. - xx, 552 p. :ill ;24 cm. - Grundlehren der mathematischen Wissenschaften,3480072-7830 ;. - Grundlehren der mathematischen Wissenschaften ;341..

Includes bibliographical references (pages 527-545) and index.

Markov semigroups -- Markov semigroups, basics and examples --

The 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 Poincaré, 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.

ISBN: 9783319002262 (hbk.) :EUR109.99

ISSN: 00727830

LCCN: 2013952461Subjects--Topical Terms:

532104
Markov processes.

LC Class. No.: QA274.7 / .B34 2014

Analysis and geometry of Markov diffusion operators /
LDR:02688cam a2200265Ii 4500 001 1900912
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008 140121s2014 sz b 001 0 eng d
010 $a 2013952461
020 $a 9783319002262 (hbk.) : $c EUR109.99
020 $a 3319002260 (hbk.)
020 $a 9783319002279 (ebk.)
020 $a 3319002279 (ebk.)
022 $a 00727830
022 $a 21969701 (ebk.)
035 $a AS-BW-103-02
040 $a CDX $b eng
050 # 4 $a QA274.7 $b .B34 2014
100 1 $a Bakry, D. $q (Dominique). $3 2024493
245 1 0 $a Analysis and geometry of Markov diffusion operators / $c by Dominique Bakry, Ivan Gentil, Michel Ledoux.
260 # $a Cham : $b Springer, $c 2014.
300 $a xx, 552 p. : $b ill ; $c 24 cm.
490 1 0 $a Grundlehren der mathematischen Wissenschaften, $x 0072-7830 ; $v 348
504 $a Includes bibliographical references (pages 527-545) and index.
505 0 # $g Markov semigroups, basics and examples -- $t Markov semigroups -- $t Model examples -- $t Symmetric Markov diffusion operators -- $g Three model functional inequalities -- $t Poincaré inequalities -- $t Logarithmic Sobolev inequalities -- $t Sobolev inequalities -- $g Related functional, isoperimetric and transportation inequalities -- $t Generalized functional inequalities -- $t Capacity and isoperimetry-type inequalities -- $t Optimal transportation and functional inequalities -- $g Appendices -- $t Appendix A : Semigroups of bounded operators on a Banach space -- $t Appendix B : Elements of stochastic calculus -- $t Appendix C : Basic notions in differential and Riemannian geometry -- $g Afterwords -- $g Notations and list of symbols.
520 # $a The 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 Poincaré, 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.
650 # 0 $a Markov processes. $3 532104
650 # 0 $a Diffusion processes. $3 648159
650 # 0 $a Markov operators. $3 752119
700 1 # $a Gentil, Ivan. $3 2024494
700 1 # $a Ledoux, Michel, $d 1958- $3 1306018
830 0 $a Grundlehren der mathematischen Wissenschaften ; $v 341. $3 1235979