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100   $a20140807d2014      u|         0
101 0 $aeng
135   $aur|n|---|||||
181   $ctxt
182   $cc
183   $acr
200 10$aSemigroups, Boundary Value Problems and Markov Processes /$fby Kazuaki Taira
205   $a2nd ed. 2014.
210  1$aBerlin, Heidelberg :$cSpringer Berlin Heidelberg :$cImprint: Springer,$d2014.
215   $a1 online resource (724 p.)
225 1 $aSpringer Monographs in Mathematics,$x1439-7382
300   $aDescription based upon print version of record.
311   $a1-322-17292-7 
311   $a3-662-43695-7 
320   $aIncludes bibliographical references and index.
327   $a1.Introduction and Main Results -- Part I Elements of Analysis -- 2.Elements of Probability Theory -- 3.Elements of Functional Analysis -- 4.Theory of Semigroups -- Part II Elements of Partial Differential Equations -- 5.Theory of Distributions -- 6.Sobolev and Besov Spaces -- 7.Theory of Pseudo-Differential Operators -- 8.Waldenfels Operators and Maximum Principles -- Part III Markov Processes, Semigroups and Boundary Value problems -- 9.Markov Processes, Transition Functions and Feller Semigroups -- 10.Feller Semigroups and Elliptic Boundary Value Problems -- 11.Proof of Theorem 1.3 -- 12.Markov Processes Revisited -- 13.Concluding Remarks -- Appendix: Boundedness of Pseudo-Differential Operators -- References -- Index.
330   $aA careful and accessible exposition of functional analytic methods in stochastic analysis is provided in this book. It focuses on the interrelationship between three subjects in analysis: Markov processes, semi groups and elliptic boundary value problems. The author studies a general class of elliptic boundary value problems for second-order, Waldenfels integro-differential operators in partial differential equations and proves that this class of elliptic boundary value problems provides a general class of Feller semigroups in functional analysis. As an application, the author constructs a general class of Markov processes in probability in which a Markovian particle moves both by jumps and continuously in the state space until it 'dies' at the time when it reaches the set where the particle is definitely absorbed. Augmenting the 1st edition published in 2004, this edition includes four new chapters and eight re-worked and expanded chapters. It is amply illustrated and all chapters are rounded off with Notes and Comments where bibliographical references are primarily discussed. Thanks to the kind feedback from many readers, some errors in the first edition have been corrected. In order to keep the book up-to-date, new references have been added to the bibliography. Researchers and graduate students interested in PDEs, functional analysis and probability will find this volume useful.
410  0$aSpringer Monographs in Mathematics,$x1439-7382
606   $aFunctional analysis
606   $aHarmonic analysis
606   $aPartial differential equations
606   $aProbabilities
606   $aFunctional Analysis$3https://scigraph.springernature.com/ontologies/product-market-codes/M12066
606   $aAbstract Harmonic Analysis$3https://scigraph.springernature.com/ontologies/product-market-codes/M12015
606   $aPartial Differential Equations$3https://scigraph.springernature.com/ontologies/product-market-codes/M12155
606   $aProbability Theory and Stochastic Processes$3https://scigraph.springernature.com/ontologies/product-market-codes/M27004
615  0$aFunctional analysis.
615  0$aHarmonic analysis.
615  0$aPartial differential equations.
615  0$aProbabilities.
615 14$aFunctional Analysis.
615 24$aAbstract Harmonic Analysis.
615 24$aPartial Differential Equations.
615 24$aProbability Theory and Stochastic Processes.
676   $a519.233
700   $aTaira$b Kazuaki$4aut$4http://id.loc.gov/vocabulary/relators/aut$059537
801  0$bMiAaPQ
801  1$bMiAaPQ
801  2$bMiAaPQ
906   $aBOOK
912   $a9910299969203321
996   $aSemigroups, boundary value problems and Markov processes$91101548
997   $aUNINA