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The Resource A Basic Course in Probability Theory, by Rabi Bhattacharya, Edward C. Waymire, (electronic resource)

A Basic Course in Probability Theory, by Rabi Bhattacharya, Edward C. Waymire, (electronic resource)

Label
A Basic Course in Probability Theory
Title
A Basic Course in Probability Theory
Statement of responsibility
by Rabi Bhattacharya, Edward C. Waymire
Creator
Contributor
Author
Subject
Language
eng
Summary
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.--
Member of
Assigning source
Provided by publisher
http://library.link/vocab/creatorName
Bhattacharya, Rabi
Image bit depth
0
Literary form
non fiction
Nature of contents
dictionaries
http://library.link/vocab/relatedWorkOrContributorName
Waymire, Edward C
Series statement
  • Universitext,
  • Springer eBooks
  • Springer eBooks.
http://library.link/vocab/subjectName
  • Distribution (Probability theory
  • Mathematics
Label
A Basic Course in Probability Theory, by Rabi Bhattacharya, Edward C. Waymire, (electronic resource)
Link
https://eui.idm.oclc.org/login?url=https://doi.org/10.1007/978-3-319-47974-3
Instantiates
Publication
Antecedent source
mixed
Carrier category
online resource
Carrier category code
  • cr
Carrier MARC source
rdacarrier
Color
not applicable
Content category
text
Content type code
  • txt
Content type MARC source
rdacontent
Contents
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
Control code
978-3-319-47974-3
Dimensions
unknown
Edition
2nd ed. 2016.
Extent
1 online resource (XII, 265 pages)
File format
multiple file formats
Form of item
  • online
  • electronic
Governing access note
Use of this electronic resource may be governed by a license agreement which restricts use to the European University Institute community. Each user is responsible for limiting use to individual, non-commercial purposes, without systematically downloading, distributing, or retaining substantial portions of information, provided that all copyright and other proprietary notices contained on the materials are retained. The use of software, including scripts, agents, or robots, is generally prohibited and may result in the loss of access to these resources for the entire European University Institute community
Isbn
9783319479743
Level of compression
uncompressed
Media category
computer
Media MARC source
rdamedia
Media type code
  • c
Quality assurance targets
absent
Reformatting quality
access
Specific material designation
remote
System control number
(OCoLC)985053912
Label
A Basic Course in Probability Theory, by Rabi Bhattacharya, Edward C. Waymire, (electronic resource)
Link
https://eui.idm.oclc.org/login?url=https://doi.org/10.1007/978-3-319-47974-3
Publication
Antecedent source
mixed
Carrier category
online resource
Carrier category code
  • cr
Carrier MARC source
rdacarrier
Color
not applicable
Content category
text
Content type code
  • txt
Content type MARC source
rdacontent
Contents
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
Control code
978-3-319-47974-3
Dimensions
unknown
Edition
2nd ed. 2016.
Extent
1 online resource (XII, 265 pages)
File format
multiple file formats
Form of item
  • online
  • electronic
Governing access note
Use of this electronic resource may be governed by a license agreement which restricts use to the European University Institute community. Each user is responsible for limiting use to individual, non-commercial purposes, without systematically downloading, distributing, or retaining substantial portions of information, provided that all copyright and other proprietary notices contained on the materials are retained. The use of software, including scripts, agents, or robots, is generally prohibited and may result in the loss of access to these resources for the entire European University Institute community
Isbn
9783319479743
Level of compression
uncompressed
Media category
computer
Media MARC source
rdamedia
Media type code
  • c
Quality assurance targets
absent
Reformatting quality
access
Specific material designation
remote
System control number
(OCoLC)985053912

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