LEADER 04712nam 22005535 450 001 9910574083003321 005 20251202133107.0 010 $a9789811910999$b(electronic bk.) 010 $z9789811910982 024 7 $a10.1007/978-981-19-1099-9 035 $a(MiAaPQ)EBC7001409 035 $a(Au-PeEL)EBL7001409 035 $a(CKB)22924498200041 035 $a(PPN)269148388 035 $a(OCoLC)1322485943 035 $a(DE-He213)978-981-19-1099-9 035 $a(EXLCZ)9922924498200041 100 $a20220528d2022 u| 0 101 0 $aeng 135 $aurcnu|||||||| 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 10$aFunctional Analytic Techniques for Diffusion Processes /$fby Kazuaki Taira 205 $a1st ed. 2022. 210 1$aSingapore :$cSpringer Nature Singapore :$cImprint: Springer,$d2022. 215 $a1 online resource (792 pages) 225 1 $aSpringer Monographs in Mathematics,$x2196-9922 300 $aIncludes index. 311 08$aPrint version: Taira, Kazuaki Functional Analytic Techniques for Diffusion Processes Singapore : Springer,c2022 9789811910982 327 $a1. Introduction and Summary -- Part I Foundations of Modern Analysis -- 2. Sets, Topology and Measures -- 3. A Short Course in Probability Theory -- 4. Manifolds, Tensors and Densities -- 5. A Short Course in Functional Analysis -- 6. A Short Course in Semigroup Theory -- Part II Elements of Partial Di?erential Equations. 7. Distributions, Operators and Kernels -- 8. L2 Theory of Sobolev Spaces -- 9. L2 Theory of Pseudo-Di?erential Operators -- Part III Maximum Principles and Elliptic Boundary Value Problems -- 10. Maximum Principles for Degenerate Elliptic Operators -- Part IV L2 Theory of Elliptic Boundary Value Problems -- 11. Elliptic Boundary Value Problems -- Part V Markov Processes, Feller Semigroups and Boundary Value Problems -- 12. Markov Processes, Transition Functions and Feller Semigroups -- 13. L2 Approach to the Construction of Feller Semigroups -- 14. Concluding Remarks -- Part VI Appendix -- A A Brief Introduction tothe Potential Theoretic Approach -- References -- Index. 330 $aThis book is an easy-to-read reference providing a link between functional analysis and diffusion processes. More precisely, the book takes readers to a mathematical crossroads of functional analysis (macroscopic approach), partial differential equations (mesoscopic approach), and probability (microscopic approach) via the mathematics needed for the hard parts of diffusion processes. This work brings these three fields of analysis together and provides a profound stochastic insight (microscopic approach) into the study of elliptic boundary value problems. The author does a massive study of diffusion processes from a broad perspective and explains mathematical matters in a more easily readable way than one usually would find. The book is amply illustrated; 14 tables and 141 figures are provided with appropriate captions in such a fashion that readers can easily understand powerful techniques of functional analysis for the study of diffusion processes in probability. The scope of the author?s work has been and continues to be powerful methods of functional analysis for future research of elliptic boundary value problems and Markov processes via semigroups. A broad spectrum of readers can appreciate easily and effectively the stochastic intuition that this book conveys. Furthermore, the book will serve as a sound basis both for researchers and for graduate students in pure and applied mathematics who are interested in a modern version of the classical potential theory and Markov processes. For advanced undergraduates working in functional analysis, partial differential equations, and probability, it provides an effective opening to these three interrelated fields of analysis. Beginning graduate students and mathematicians in the field looking for a coherent overview will find the book to be a helpful beginning. This work will be a major influence in a very broad field of study for a long time. 410 0$aSpringer Monographs in Mathematics,$x2196-9922 606 $aFunctional analysis 606 $aProbabilities 606 $aFunctional Analysis 606 $aProbability Theory 615 0$aFunctional analysis. 615 0$aProbabilities. 615 14$aFunctional Analysis. 615 24$aProbability Theory. 676 $a519.233 700 $aTaira$b Kazuaki$059537 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 912 $a9910574083003321 996 $aFunctional Analytic Techniques for Diffusion Processes$92876446 997 $aUNINA