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Probability theory = a comprehensive...

Klenke, Achim.

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Probability theory = a comprehensive course /

紀錄類型:	書目-電子資源 : Monograph/item
正題名/作者:	Probability theory/ by Achim Klenke.
其他題名:	a comprehensive course /
作者:	Klenke, Achim.
出版者:	Cham :Springer International Publishing : : 2020.,
面頁冊數:	xiv, 716 p. :ill., digital ;24 cm.
內容註:	1 Basic Measure Theory -- 2 Independence -- 3 Generating Functions -- 4 The Integral -- 5 Moments and Laws of Large Numbers -- 6 Convergence Theorems -- 7 Lp-Spaces and the Radon-Nikodym Theorem -- 8 Conditional Expectations -- 9 Martingales -- 10 Optional Sampling Theorems -- 11 Martingale Convergence Theorems and Their Applications -- 12 Backwards Martingales and Exchangeability -- 13 Convergence of Measures -- 14 Probability Measures on Product Spaces -- 15 Characteristic Functions and the Central Limit Theorem -- 16 Infinitely Divisible Distributions -- 17 Markov Chains -- 18 Convergence of Markov Chains -- 19 Markov Chains and Electrical Networks -- 20 Ergodic Theory -- 21 Brownian Motion -- 22 Law of the Iterated Logarithm -- 23 Large Deviations -- 24 The Poisson Point Process -- 25 The Ito Integral -- 26 Stochastic Differential Equations -- References -- Notation Index -- Name Index -- Subject Index.
Contained By:	Springer Nature eBook
標題:	Probabilities. -
電子資源:	https://doi.org/10.1007/978-3-030-56402-5
ISBN:	9783030564025

Probability theory = a comprehensive course /
Klenke, Achim.

Probability theorya comprehensive course /[electronic resource] :by Achim Klenke. - Third edition. - Cham :Springer International Publishing :2020. - xiv, 716 p. :ill., digital ;24 cm. - Universitext,0172-5939. - Universitext..

1 Basic Measure Theory -- 2 Independence -- 3 Generating Functions -- 4 The Integral -- 5 Moments and Laws of Large Numbers -- 6 Convergence Theorems -- 7 Lp-Spaces and the Radon-Nikodym Theorem -- 8 Conditional Expectations -- 9 Martingales -- 10 Optional Sampling Theorems -- 11 Martingale Convergence Theorems and Their Applications -- 12 Backwards Martingales and Exchangeability -- 13 Convergence of Measures -- 14 Probability Measures on Product Spaces -- 15 Characteristic Functions and the Central Limit Theorem -- 16 Infinitely Divisible Distributions -- 17 Markov Chains -- 18 Convergence of Markov Chains -- 19 Markov Chains and Electrical Networks -- 20 Ergodic Theory -- 21 Brownian Motion -- 22 Law of the Iterated Logarithm -- 23 Large Deviations -- 24 The Poisson Point Process -- 25 The Ito Integral -- 26 Stochastic Differential Equations -- References -- Notation Index -- Name Index -- Subject Index.

This popular textbook, now in a revised and expanded third edition, presents a comprehensive course in modern probability theory. Probability plays an increasingly important role not only in mathematics, but also in physics, biology, finance and computer science, helping to understand phenomena such as magnetism, genetic diversity and market volatility, and also to construct efficient algorithms. Starting with the very basics, this textbook covers a wide variety of topics in probability, including many not usually found in introductory books, such as: limit theorems for sums of random variables martingales percolation Markov chains and electrical networks construction of stochastic processes Poisson point process and infinite divisibility large deviation principles and statistical physics Brownian motion stochastic integrals and stochastic differential equations. The presentation is self-contained and mathematically rigorous, with the material on probability theory interspersed with chapters on measure theory to better illustrate the power of abstract concepts. This third edition has been carefully extended and includes new features, such as concise summaries at the end of each section and additional questions to encourage self-reflection, as well as updates to the figures and computer simulations. With a wealth of examples and more than 290 exercises, as well as biographical details of key mathematicians, it will be of use to students and researchers in mathematics, statistics, physics, computer science, economics and biology.

ISBN: 9783030564025

Standard No.: 10.1007/978-3-030-56402-5doiSubjects--Topical Terms:

518889
Probabilities.

LC Class. No.: QA273.18

Dewey Class. No.: 519.2

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505 0 $a 1 Basic Measure Theory -- 2 Independence -- 3 Generating Functions -- 4 The Integral -- 5 Moments and Laws of Large Numbers -- 6 Convergence Theorems -- 7 Lp-Spaces and the Radon-Nikodym Theorem -- 8 Conditional Expectations -- 9 Martingales -- 10 Optional Sampling Theorems -- 11 Martingale Convergence Theorems and Their Applications -- 12 Backwards Martingales and Exchangeability -- 13 Convergence of Measures -- 14 Probability Measures on Product Spaces -- 15 Characteristic Functions and the Central Limit Theorem -- 16 Infinitely Divisible Distributions -- 17 Markov Chains -- 18 Convergence of Markov Chains -- 19 Markov Chains and Electrical Networks -- 20 Ergodic Theory -- 21 Brownian Motion -- 22 Law of the Iterated Logarithm -- 23 Large Deviations -- 24 The Poisson Point Process -- 25 The Ito Integral -- 26 Stochastic Differential Equations -- References -- Notation Index -- Name Index -- Subject Index.
520 $a This popular textbook, now in a revised and expanded third edition, presents a comprehensive course in modern probability theory. Probability plays an increasingly important role not only in mathematics, but also in physics, biology, finance and computer science, helping to understand phenomena such as magnetism, genetic diversity and market volatility, and also to construct efficient algorithms. Starting with the very basics, this textbook covers a wide variety of topics in probability, including many not usually found in introductory books, such as: limit theorems for sums of random variables martingales percolation Markov chains and electrical networks construction of stochastic processes Poisson point process and infinite divisibility large deviation principles and statistical physics Brownian motion stochastic integrals and stochastic differential equations. The presentation is self-contained and mathematically rigorous, with the material on probability theory interspersed with chapters on measure theory to better illustrate the power of abstract concepts. This third edition has been carefully extended and includes new features, such as concise summaries at the end of each section and additional questions to encourage self-reflection, as well as updates to the figures and computer simulations. With a wealth of examples and more than 290 exercises, as well as biographical details of key mathematicians, it will be of use to students and researchers in mathematics, statistics, physics, computer science, economics and biology.
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