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)
Resource Information
The item A Basic Course in Probability Theory, by Rabi Bhattacharya, Edward C. Waymire, (electronic resource) represents a specific, individual, material embodiment of a distinct intellectual or artistic creation found in European University Institute.This item is available to borrow from 1 library branch.
Resource Information
The item A Basic Course in Probability Theory, by Rabi Bhattacharya, Edward C. Waymire, (electronic resource) represents a specific, individual, material embodiment of a distinct intellectual or artistic creation found in European University Institute.
This item is available to borrow from 1 library branch.
 Summary
 This text develops the necessary background in probability theory underlying diverse treatments of stochastic processes and their wideranging 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 coauthored numerous books, including a series of four upcoming graduate textbooks in stochastic processes with applications.
 Language
 eng
 Edition
 2nd ed. 2016.
 Extent
 1 online resource (XII, 265 pages)
 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 ZeroOne 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 FineScale 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
 Isbn
 9783319479743
 Label
 A Basic Course in Probability Theory
 Title
 A Basic Course in Probability Theory
 Statement of responsibility
 by Rabi Bhattacharya, Edward C. Waymire
 Language
 eng
 Summary
 This text develops the necessary background in probability theory underlying diverse treatments of stochastic processes and their wideranging 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 coauthored numerous books, including a series of four upcoming graduate textbooks in stochastic processes with applications.
 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)
 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 ZeroOne 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 FineScale 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
 9783319479743
 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, noncommercial 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)
 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 ZeroOne 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 FineScale 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
 9783319479743
 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, noncommercial 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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<div class="citation" vocab="http://schema.org/"><i class="fa faexternallinksquare fafw"></i> Data from <span resource="http://link.library.eui.eu/portal/ABasicCourseinProbabilityTheorybyRabi/2gSmUlLPZwQ/" typeof="Book http://bibfra.me/vocab/lite/Item"><span property="name http://bibfra.me/vocab/lite/label"><a href="http://link.library.eui.eu/portal/ABasicCourseinProbabilityTheorybyRabi/2gSmUlLPZwQ/">A Basic Course in Probability Theory, by Rabi Bhattacharya, Edward C. Waymire, (electronic resource)</a></span>  <span property="potentialAction" typeOf="OrganizeAction"><span property="agent" typeof="LibrarySystem http://library.link/vocab/LibrarySystem" resource="http://link.library.eui.eu/"><span property="name http://bibfra.me/vocab/lite/label"><a property="url" href="http://link.library.eui.eu/">European University Institute</a></span></span></span></span></div>