國立虎尾科技大學 |

Measure-theoretic probability = with applications to statistics, finance, and engineering /

紀錄類型:	書目-語言資料,印刷品 : Monograph/item
正題名/作者:	Measure-theoretic probability/ by Kenneth Shum.
其他題名:	with applications to statistics, finance, and engineering /
作者:	Shum, Kenneth.
出版者:	Cham :Springer International Publishing : : 2023.,
面頁冊數:	xv, 259 p. :ill. (chiefly color), digital ; : 24 cm.;
Contained By:	Springer Nature eBook
標題:	Measure and Integration. -
電子資源:	https://doi.org/10.1007/978-3-031-49830-5
ISBN:	9783031498305

Measure-theoretic probability = with applications to statistics, finance, and engineering /
Shum, Kenneth.

Measure-theoretic probabilitywith applications to statistics, finance, and engineering /[electronic resource] :by Kenneth Shum. - Cham :Springer International Publishing :2023. - xv, 259 p. :ill. (chiefly color), digital ;24 cm. - Compact textbooks in mathematics,2296-455X. - Compact textbooks in mathematics..

Preface -- Beyond discrete and continuous random variables -- Probability spaces -- Lebesgue-Stieltjes measures -- Measurable functions and random variables -- Statistical independence -- Lebesgue integral and mathematical expectation -- Properties of Lebesgue integral and convergence theorems -- Product space and coupling -- Moment generating functions and characteristic functions -- Modes of convergence -- Laws of large numbers -- Techniques from Hilbert space theory -- Conditional expectation -- Levy's continuity theorem and central limit theorem -- References -- Index.

This textbook offers an approachable introduction to measure-theoretic probability, illustrating core concepts with examples from statistics and engineering. The author presents complex concepts in a succinct manner, making otherwise intimidating material approachable to undergraduates who are not necessarily studying mathematics as their major. Throughout, readers will learn how probability serves as the language in a variety of exciting fields. Specific applications covered include the coupon collector's problem, Monte Carlo integration in finance, data compression in information theory, and more. Measure-Theoretic Probability is ideal for a one-semester course and will best suit undergraduates studying statistics, data science, financial engineering, and economics who want to understand and apply more advanced ideas from probability to their disciplines. As a concise and rigorous introduction to measure-theoretic probability, it is also suitable for self-study. Prerequisites include a basic knowledge of probability and elementary concepts from real analysis.

ISBN: 9783031498305

Standard No.: 10.1007/978-3-031-49830-5doiSubjects--Topical Terms:

672015
Measure and Integration.

LC Class. No.: QA273 / .S48 2023

Dewey Class. No.: 519.2

Measure-theoretic probability = with applications to statistics, finance, and engineering /
LDR:02801nam a2200361 a 4500 001 1120891
003 DE-He213
005 20240213112457.0
006 m d
007 cr nn 008maaau
008 240612s2023 sz s 0 eng d
020 $a 9783031498305 $q (electronic bk.)
020 $a 9783031498329 $q (paper)
024 7 $a 10.1007/978-3-031-49830-5 $2 doi
035 $a 978-3-031-49830-5
040 $a GP $c GP
041 0 $a eng
050 4 $a QA273 $b .S48 2023
072 7 $a PBT $2 bicssc
072 7 $a PBWL $2 bicssc
072 7 $a MAT029000 $2 bisacsh
072 7 $a PBT $2 thema
072 7 $a PBWL $2 thema
082 0 4 $a 519.2 $2 23
090 $a QA273 $b .S562 2023
100 1 $a Shum, Kenneth. $3 1436466
245 1 0 $a Measure-theoretic probability $h [electronic resource] : $b with applications to statistics, finance, and engineering / $c by Kenneth Shum.
260 $a Cham : $b Springer International Publishing : $b Imprint: Birkhäuser, $c 2023.
300 $a xv, 259 p. : $b ill. (chiefly color), digital ; $c 24 cm.
490 1 $a Compact textbooks in mathematics, $x 2296-455X
505 0 $a Preface -- Beyond discrete and continuous random variables -- Probability spaces -- Lebesgue-Stieltjes measures -- Measurable functions and random variables -- Statistical independence -- Lebesgue integral and mathematical expectation -- Properties of Lebesgue integral and convergence theorems -- Product space and coupling -- Moment generating functions and characteristic functions -- Modes of convergence -- Laws of large numbers -- Techniques from Hilbert space theory -- Conditional expectation -- Levy's continuity theorem and central limit theorem -- References -- Index.
520 $a This textbook offers an approachable introduction to measure-theoretic probability, illustrating core concepts with examples from statistics and engineering. The author presents complex concepts in a succinct manner, making otherwise intimidating material approachable to undergraduates who are not necessarily studying mathematics as their major. Throughout, readers will learn how probability serves as the language in a variety of exciting fields. Specific applications covered include the coupon collector's problem, Monte Carlo integration in finance, data compression in information theory, and more. Measure-Theoretic Probability is ideal for a one-semester course and will best suit undergraduates studying statistics, data science, financial engineering, and economics who want to understand and apply more advanced ideas from probability to their disciplines. As a concise and rigorous introduction to measure-theoretic probability, it is also suitable for self-study. Prerequisites include a basic knowledge of probability and elementary concepts from real analysis.
650 2 4 $a Measure and Integration. $3 672015
650 2 4 $a Applied Probability. $3 1390075
650 1 4 $a Probability Theory. $3 1366244
650 0 $a Probabilities. $3 527847
710 2 $a SpringerLink (Online service) $3 593884
773 0 $t Springer Nature eBook
830 0 $a Compact textbooks in mathematics. $3 1069870
856 4 0 $u https://doi.org/10.1007/978-3-031-49830-5
950 $a Mathematics and Statistics (SpringerNature-11649)