LEADER 04010nam 22006135 450 001 9910624396803321 005 20251113200943.0 010 $a9783031142055$b(electronic bk.) 010 $z9783031142048 024 7 $a10.1007/978-3-031-14205-5 035 $a(MiAaPQ)EBC7127772 035 $a(Au-PeEL)EBL7127772 035 $a(CKB)25219376900041 035 $a(PPN)26585640X 035 $a(OCoLC)1350250998 035 $a(DE-He213)978-3-031-14205-5 035 $a(EXLCZ)9925219376900041 100 $a20221029d2022 u| 0 101 0 $aeng 135 $aurcnu|||||||| 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 10$aMeasure Theory, Probability, and Stochastic Processes /$fby Jean-François Le Gall 205 $a1st ed. 2022. 210 1$aCham :$cSpringer International Publishing :$cImprint: Springer,$d2022. 215 $a1 online resource (409 pages) 225 1 $aGraduate Texts in Mathematics,$x2197-5612 ;$v295 311 08$aPrint version: 9783031142048 320 $aIncludes bibliographical references (pages 401-402) and index. 327 $aPart I. Measure Theory -- Chapter 1. Measurable Spaces -- Chapter 2. Integration of Measurable Functions -- Chapter 3. Construction of Measures -- Chapter 4. Lp Spaces -- Chapter 5. Product Measure -- Chapter 6. Signed Measures -- Chapter 7. Change of Variables -- Part II. Probability Theory -- Chapter 8. Foundations of Probability Theory -- Chapter 9. Independence -- Chapter 10. Convergence of Random Variables -- Chapter 11. Conditioning -- Part III. Stochastic Processes -- Chapter 12. Theory of Martingales -- Chapter 13. Markov Chains -- Chapter 14. Brownian Motion. . 330 $aThis textbook introduces readers to the fundamental notions of modern probability theory. The only prerequisite is a working knowledge in real analysis. Highlighting the connections between martingales and Markov chains on one hand, and Brownian motion and harmonic functions on the other, this book provides an introduction to the rich interplay between probability and other areas of analysis. Arranged into three parts, the book begins with a rigorous treatment of measure theory, with applications to probability in mind. The second part of the book focuses on the basic concepts of probability theory such as random variables, independence, conditional expectation, and the different types of convergence of random variables. In the third part, in which all chapters can be read independently, the reader will encounter three important classes of stochastic processes: discrete-time martingales, countable state-space Markov chains, and Brownian motion. Each chapter ends with a selection of illuminating exercises of varying difficulty. Some basic facts from functional analysis, in particular on Hilbert and Banach spaces, are included in the appendix. Measure Theory, Probability, and Stochastic Processes is an ideal text for readers seeking a thorough understanding of basic probability theory. Students interested in learning more about Brownian motion, and other continuous-time stochastic processes, may continue reading the author?s more advanced textbook in the same series (GTM 274). 410 0$aGraduate Texts in Mathematics,$x2197-5612 ;$v295 606 $aMeasure theory 606 $aProbabilities 606 $aStochastic processes 606 $aMeasure and Integration 606 $aProbability Theory 606 $aStochastic Processes 615 0$aMeasure theory. 615 0$aProbabilities. 615 0$aStochastic processes. 615 14$aMeasure and Integration. 615 24$aProbability Theory. 615 24$aStochastic Processes. 676 $a515.42 676 $a519.2 700 $aLe Gall$b J. F$g(Jean-Franc?ois),$0348889 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 912 $a9910624396803321 996 $aMeasure Theory, Probability, and Stochastic Processes$92963436 997 $aUNINA