國立高雄大學圖資館 |

Language: English

Back

A basic course in probability theory

Bhattacharya, Rabi.

A basic course in probability theory

Record Type:	Electronic resources : Monograph/item
Title/Author:	A basic course in probability theoryby Rabi Bhattacharya, Edward C. Waymire.
Author:	Bhattacharya, Rabi.
other author:	Waymire, Edward C.
Published:	Cham :Springer International Publishing :2016.
Description:	xii, 265 p. :ill., digital ;24 cm.
Contained By:	Springer eBooks
Subject:	Probabilities.
Online resource:	http://dx.doi.org/10.1007/978-3-319-47974-3
ISBN:	9783319479743$q(electronic bk.)

A basic course in probability theory
Bhattacharya, Rabi.

A basic course in probability theory[electronic resource] /by Rabi Bhattacharya, Edward C. Waymire. - 2nd ed. - Cham :Springer International Publishing :2016. - xii, 265 p. :ill., digital ;24 cm. - Universitext,0172-5939. - Universitext..

Preface to Second Edition -- Preface to First Edition -- I. Random Maps, Distribution, and Mathematical Expectation -- II. Independence, Conditional Expectation -- III. Martingales and Stopping Times -- IV. Classical Central Limit Theorems -- V. Classical Zero-One Laws, Laws of Large Numbers and Large Deviations -- VI. Fourier Series, Fourier Transform, and Characteristic Functions -- VII. Weak Convergence of Probability Measures on Metric Spaces -- VIII. Random Series of Independent Summands -- IX. Kolmogorov's Extension Theorem and Brownian Motion -- X. Brownian Motion: The LIL and Some Fine-Scale Properties -- XI. Strong Markov Property, Skorokhod Embedding and Donsker's Invariance Principle -- XII. A Historical Note on Brownian Motion -- XIII. Some Elements of the Theory of Markov Processes and their Convergence to Equilibrium -- A. Measure and Integration -- B. Topology and Function Spaces -- C. Hilbert Spaces and Applications in Measure Theory -- References -- Symbol Index -- Subject Index.

This text develops the necessary background in probability theory underlying diverse treatments of stochastic processes and their wide-ranging applications. In this second edition, the text has been reorganized for didactic purposes, new exercises have been added and basic theory has been expanded. General Markov dependent sequences and their convergence to equilibrium is the subject of an entirely new chapter. The introduction of conditional expectation and conditional probability very early in the text maintains the pedagogic innovation of the first edition; conditional expectation is illustrated in detail in the context of an expanded treatment of martingales, the Markov property, and the strong Markov property. Weak convergence of probabilities on metric spaces and Brownian motion are two topics to highlight. A selection of large deviation and/or concentration inequalities ranging from those of Chebyshev, Cramer-Chernoff, Bahadur-Rao, to Hoeffding have been added, with illustrative comparisons of their use in practice. This also includes a treatment of the Berry-Esseen error estimate in the central limit theorem. The authors assume mathematical maturity at a graduate level; otherwise the book is suitable for students with varying levels of background in analysis and measure theory. For the reader who needs refreshers, theorems from analysis and measure theory used in the main text are provided in comprehensive appendices, along with their proofs, for ease of reference. Rabi Bhattacharya is Professor of Mathematics at the University of Arizona. Edward Waymire is Professor of Mathematics at Oregon State University. Both authors have co-authored numerous books, including a series of four upcoming graduate textbooks in stochastic processes with applications.

ISBN: 9783319479743$q(electronic bk.)

Standard No.: 10.1007/978-3-319-47974-3doiSubjects--Topical Terms:

182046
Probabilities.

LC Class. No.: QA273

Dewey Class. No.: 519.2

A basic course in probability theory
LDR:03827nmm a2200349 a 4500 001 502505
003 DE-He213
005 20170214093901.0
006 m d
007 cr nn 008maaau
008 170823s2016 gw s 0 eng d
020 $a 9783319479743$q(electronic bk.)
020 $a 9783319479729$q(paper)
024 7 $a 10.1007/978-3-319-47974-3 $2 doi
035 $a 978-3-319-47974-3
040 $a GP $c GP
041 0 $a eng
050 4 $a QA273
072 7 $a PBT $2 bicssc
072 7 $a PBWL $2 bicssc
072 7 $a MAT029000 $2 bisacsh
082 0 4 $a 519.2 $2 23
090 $a QA273 $b .B575 2016
100 1 $a Bhattacharya, Rabi. $3 322890
245 1 2 $a A basic course in probability theory $h [electronic resource] / $c by Rabi Bhattacharya, Edward C. Waymire.
250 $a 2nd ed.
260 $a Cham : $b Springer International Publishing : $b Imprint: Springer, $c 2016.
300 $a xii, 265 p. : $b ill., digital ; $c 24 cm.
490 1 $a Universitext, $x 0172-5939
505 0 $a Preface to Second Edition -- Preface to First Edition -- I. Random Maps, Distribution, and Mathematical Expectation -- II. Independence, Conditional Expectation -- III. Martingales and Stopping Times -- IV. Classical Central Limit Theorems -- V. Classical Zero-One Laws, Laws of Large Numbers and Large Deviations -- VI. Fourier Series, Fourier Transform, and Characteristic Functions -- VII. Weak Convergence of Probability Measures on Metric Spaces -- VIII. Random Series of Independent Summands -- IX. Kolmogorov's Extension Theorem and Brownian Motion -- X. Brownian Motion: The LIL and Some Fine-Scale Properties -- XI. Strong Markov Property, Skorokhod Embedding and Donsker's Invariance Principle -- XII. A Historical Note on Brownian Motion -- XIII. Some Elements of the Theory of Markov Processes and their Convergence to Equilibrium -- A. Measure and Integration -- B. Topology and Function Spaces -- C. Hilbert Spaces and Applications in Measure Theory -- References -- Symbol Index -- Subject Index.
520 $a This text develops the necessary background in probability theory underlying diverse treatments of stochastic processes and their wide-ranging applications. In this second edition, the text has been reorganized for didactic purposes, new exercises have been added and basic theory has been expanded. General Markov dependent sequences and their convergence to equilibrium is the subject of an entirely new chapter. The introduction of conditional expectation and conditional probability very early in the text maintains the pedagogic innovation of the first edition; conditional expectation is illustrated in detail in the context of an expanded treatment of martingales, the Markov property, and the strong Markov property. Weak convergence of probabilities on metric spaces and Brownian motion are two topics to highlight. A selection of large deviation and/or concentration inequalities ranging from those of Chebyshev, Cramer-Chernoff, Bahadur-Rao, to Hoeffding have been added, with illustrative comparisons of their use in practice. This also includes a treatment of the Berry-Esseen error estimate in the central limit theorem. The authors assume mathematical maturity at a graduate level; otherwise the book is suitable for students with varying levels of background in analysis and measure theory. For the reader who needs refreshers, theorems from analysis and measure theory used in the main text are provided in comprehensive appendices, along with their proofs, for ease of reference. Rabi Bhattacharya is Professor of Mathematics at the University of Arizona. Edward Waymire is Professor of Mathematics at Oregon State University. Both authors have co-authored numerous books, including a series of four upcoming graduate textbooks in stochastic processes with applications.
650 0 $a Probabilities. $3 182046
650 1 4 $a Mathematics. $3 184409
650 2 4 $a Probability Theory and Stochastic Processes. $3 274061
650 2 4 $a Measure and Integration. $3 273777
700 1 $a Waymire, Edward C. $3 245505
710 2 $a SpringerLink (Online service) $3 273601
773 0 $t Springer eBooks
830 0 $a Universitext. $3 558272
856 4 0 $u http://dx.doi.org/10.1007/978-3-319-47974-3
950 $a Mathematics and Statistics (Springer-11649)