國立高雄大學圖資館 |

登入

回首頁

Measure theory, probability, and stochastic processes

紀錄類型:	書目-電子資源 : Monograph/item
正題名/作者:	Measure theory, probability, and stochastic processesby Jean-Francois Le Gall.
作者:	Le Gall, Jean-Francois.
出版者:	Cham :Springer International Publishing :2022.
面頁冊數:	xiv, 406 p. :ill., digital ;24 cm.
Contained By:	Springer Nature eBook
標題:	Measure theory.
電子資源:	https://doi.org/10.1007/978-3-031-14205-5
ISBN:	9783031142055$q(electronic bk.)

Measure theory, probability, and stochastic processes
Le Gall, Jean-Francois.

Measure theory, probability, and stochastic processes[electronic resource] /by Jean-Francois Le Gall. - Cham :Springer International Publishing :2022. - xiv, 406 p. :ill., digital ;24 cm. - Graduate texts in mathematics,2952197-5612 ;. - Graduate texts in mathematics ;129..

Part 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.

This 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)

ISBN: 9783031142055$q(electronic bk.)

Standard No.: 10.1007/978-3-031-14205-5doiSubjects--Topical Terms:

182047
Measure theory.

LC Class. No.: QA312 / .L4 2022

Dewey Class. No.: 515.42

Measure theory, probability, and stochastic processes
LDR:03123nmm a2200337 a 4500 001 631549
003 DE-He213
005 20221029115129.0
006 m d
007 cr nn 008maaau
008 230411s2022 sz s 0 eng d
020 $a 9783031142055$q(electronic bk.)
020 $a 9783031142048$q(paper)
024 7 $a 10.1007/978-3-031-14205-5 $2 doi
035 $a 978-3-031-14205-5
040 $a GP $c GP
041 0 $a eng
050 4 $a QA312 $b .L4 2022
072 7 $a PBKL $2 bicssc
072 7 $a MAT034000 $2 bisacsh
072 7 $a PBKL $2 thema
082 0 4 $a 515.42 $2 23
090 $a QA312 $b .L496 2022
100 1 $a Le Gall, Jean-Francois. $3 745067
245 1 0 $a Measure theory, probability, and stochastic processes $h [electronic resource] / $c by Jean-Francois Le Gall.
260 $a Cham : $b Springer International Publishing : $b Imprint: Springer, $c 2022.
300 $a xiv, 406 p. : $b ill., digital ; $c 24 cm.
490 1 $a Graduate texts in mathematics, $x 2197-5612 ; $v 295
505 0 $a Part 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.
520 $a This 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)
650 0 $a Measure theory. $3 182047
650 0 $a Probabilities. $3 182046
650 0 $a Stochastic processes. $3 181874
650 1 4 $a Measure and Integration. $3 273777
650 2 4 $a Probability Theory. $3 913371
650 2 4 $a Stochastic Processes. $3 743764
710 2 $a SpringerLink (Online service) $3 273601
773 0 $t Springer Nature eBook
830 0 $a Graduate texts in mathematics ; $v 129. $3 436082
856 4 0 $u https://doi.org/10.1007/978-3-031-14205-5
950 $a Mathematics and Statistics (SpringerNature-11649)