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
Author
Subject
Language
  • eng
  • eng
Summary
The book develops the necessary background in probability theory underlying diverse treatments of stochastic processes and their wide-ranging applications. With this goal in mind, the pace is lively, yet thorough. Basic notions of independence and conditional expectation are introduced relatively early on in the text, while conditional expectation is illustrated in detail in the context of martingales, Markov property and strong Markov property. Weak convergence of probabilities on metric spaces and Brownian motion are two highlights. The historic role of size-biasing is emphasized in the contexts of large deviations and in developments of Tauberian Theory. The authors assume a graduate level of maturity in mathematics, but otherwise the book will be suitable for students with varying levels of background in analysis and measure theory. In particular, 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 the graduate textbook, Stochastic Processes with Applications
Member of
Is Subseries of
http://library.link/vocab/creatorName
Bhattacharya, Rabi
Dewey number
519.2
http://bibfra.me/vocab/relation/httpidlocgovvocabularyrelatorsaut
  • 7OUNbyuNZu0
  • tDhJzW4oDDI
Language note
English
LC call number
  • QA273.A1-274.9
  • QA274-274.9
Literary form
non fiction
Nature of contents
dictionaries
http://library.link/vocab/relatedWorkOrContributorName
Waymire, Edward C.
Series statement
Universitext,
http://library.link/vocab/subjectName
  • Distribution (Probability theory
  • Mathematics
  • Global analysis (Mathematics)
  • Probability Theory and Stochastic Processes
  • Measure and Integration
  • Analysis
Label
A Basic Course in Probability Theory, by Rabi Bhattacharya, Edward C. Waymire, (electronic resource)
Instantiates
Publication
Note
Description based upon print version of record
Bibliography note
Includes bibliographical references (p. [201]-204) and index
Carrier category
online resource
Carrier category code
cr
Content category
text
Content type code
txt
Contents
Random Maps, Distribution, and Mathematical Expectation -- Independence, Conditional Expectation -- Martingales and Stopping Times -- Classical Zero–One Laws, Laws of Large Numbers and Deviations -- Weak Convergence of Probability Measures -- Fourier Series, Fourier Transform, and Characteristic Functions -- Classical Central Limit Theorems -- Laplace Transforms and Tauberian Theorem -- Random Series of Independent Summands -- Kolmogorov's Extension Theorem and Brownian Motion -- Brownian Motion: The LIL and Some Fine-Scale Properties -- Skorokhod Embedding and Donsker's Invariance Principle -- A Historical Note on Brownian Motion
Dimensions
unknown
Edition
1st ed. 2007.
Extent
1 online resource (216 p.)
Form of item
online
Isbn
9780387719399
Media category
computer
Media type code
c
Other control number
10.1007/978-0-387-71939-9
Specific material designation
remote
System control number
  • (CKB)1000000000491954
  • (EBL)3062687
  • (SSID)ssj0000316440
  • (PQKBManifestationID)11223742
  • (PQKBTitleCode)TC0000316440
  • (PQKBWorkID)10275219
  • (PQKB)11503626
  • (DE-He213)978-0-387-71939-9
  • (MiAaPQ)EBC3062687
  • (EXLCZ)991000000000491954
Label
A Basic Course in Probability Theory, by Rabi Bhattacharya, Edward C. Waymire, (electronic resource)
Publication
Note
Description based upon print version of record
Bibliography note
Includes bibliographical references (p. [201]-204) and index
Carrier category
online resource
Carrier category code
cr
Content category
text
Content type code
txt
Contents
Random Maps, Distribution, and Mathematical Expectation -- Independence, Conditional Expectation -- Martingales and Stopping Times -- Classical Zero–One Laws, Laws of Large Numbers and Deviations -- Weak Convergence of Probability Measures -- Fourier Series, Fourier Transform, and Characteristic Functions -- Classical Central Limit Theorems -- Laplace Transforms and Tauberian Theorem -- Random Series of Independent Summands -- Kolmogorov's Extension Theorem and Brownian Motion -- Brownian Motion: The LIL and Some Fine-Scale Properties -- Skorokhod Embedding and Donsker's Invariance Principle -- A Historical Note on Brownian Motion
Dimensions
unknown
Edition
1st ed. 2007.
Extent
1 online resource (216 p.)
Form of item
online
Isbn
9780387719399
Media category
computer
Media type code
c
Other control number
10.1007/978-0-387-71939-9
Specific material designation
remote
System control number
  • (CKB)1000000000491954
  • (EBL)3062687
  • (SSID)ssj0000316440
  • (PQKBManifestationID)11223742
  • (PQKBTitleCode)TC0000316440
  • (PQKBWorkID)10275219
  • (PQKB)11503626
  • (DE-He213)978-0-387-71939-9
  • (MiAaPQ)EBC3062687
  • (EXLCZ)991000000000491954

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