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Measure-theoretic probabilitywith applications to statistics, finance, and engineering /

紀錄類型:	書目-電子資源 : Monograph/item
正題名/作者:	Measure-theoretic probabilityby 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:	Probabilities.
電子資源:	https://doi.org/10.1007/978-3-031-49830-5
ISBN:	9783031498305$q(electronic bk.)

Measure-theoretic probabilitywith 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$q(electronic bk.)

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

182046
Probabilities.

LC Class. No.: QA273 / .S48 2023

Dewey Class. No.: 519.2

Measure-theoretic probabilitywith applications to statistics, finance, and engineering /
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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.
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