The Resource Probability Theory : A Comprehensive Course, by Achim Klenke, (electronic resource)

Probability Theory : A Comprehensive Course, by Achim Klenke, (electronic resource)

Label
Probability Theory : A Comprehensive Course
Title
Probability Theory
Title remainder
A Comprehensive Course
Statement of responsibility
by Achim Klenke
Creator
Author
Author
Subject
Language
  • eng
  • eng
Summary
Probabilistic concepts play an increasingly important role in mathematics, physics, biology, financial engineering and computer science. They help us to understand magnetism, amorphous media, genetic diversity and the perils of random developments on the financial markets, and they guide us in constructing more efficient algorithms. This text is a comprehensive course in modern probability theory and its measure-theoretical foundations. Aimed primarily at graduate students and researchers, the book covers a wide variety of topics, many of which are not usually found in introductory textbooks, such as: limit theorems for sums of random variables; martingales; percolation; Markov chains and electrical networks; construction of stochastic processes; Poisson point processes and infinite divisibility; large deviation principles and statistical physics; Brownian motion; and stochastic integral and stochastic differential equations. The theory is developed rigorously and in a self-contained way, with the chapters on measure theory interlaced with the probabilistic chapters in order to display the power of the abstract concepts in the world of probability theory. In addition, plenty of figures, computer simulations, biographic details of key mathematicians, and a wealth of examples support and enliven the presentation
Member of
Is Subseries of
http://library.link/vocab/creatorName
Klenke, Achim
Dewey number
519.2
http://bibfra.me/vocab/relation/httpidlocgovvocabularyrelatorsaut
T7Vl_7bSCCE
Language note
English
LC call number
  • QA273.A1-274.9
  • QA274-274.9
Literary form
non fiction
Nature of contents
dictionaries
Series statement
Universitext,
http://library.link/vocab/subjectName
  • Distribution (Probability theory
  • Mathematical statistics
  • Statistical physics
  • Probability Theory and Stochastic Processes
  • Statistical Theory and Methods
  • Complex Systems
  • Statistical Physics and Dynamical Systems
Label
Probability Theory : A Comprehensive Course, by Achim Klenke, (electronic resource)
Instantiates
Publication
Note
Description based upon print version of record
Bibliography note
Includes bibliographical references (p. [591]-598) and indexes
Carrier category
online resource
Carrier category code
cr
Content category
text
Content type code
txt
Contents
Basic Measure Theory -- Independence -- Generating Functions -- The Integral -- Moments and Laws of Large Numbers -- Convergence Theorems -- Lp-Spaces and the Radon-Nikodym Theorem -- Conditional Expectations -- Martingales -- Optional Sampling Theorems -- Martingale Convergence Theorems and Their Applications -- Backwards Martingales and Exchangeability -- Convergence of Measures -- Probability Measures on Product Spaces -- Characteristic Functions and the Central Limit Theorem -- Infinitely Divisible Distributions -- Markov Chains -- Convergence of Markov Chains -- Markov Chains and Electrical Networks -- Ergodic Theory -- Brownian Motion -- Law of the Iterated Logarithm -- Large Deviations -- The Poisson Point Process -- The Itô Integral -- Stochastic Differential Equations
Dimensions
unknown
Edition
1st ed. 2008.
Extent
1 online resource (620 p.)
Form of item
online
Isbn
9781848000483
Media category
computer
Media type code
c
Other control number
10.1007/978-1-84800-048-3
Specific material designation
remote
System control number
  • (CKB)1000000000492084
  • (EBL)3062906
  • (SSID)ssj0000319576
  • (PQKBManifestationID)11252066
  • (PQKBTitleCode)TC0000319576
  • (PQKBWorkID)10338645
  • (PQKB)10950712
  • (DE-He213)978-1-84800-048-3
  • (MiAaPQ)EBC3062906
  • (EXLCZ)991000000000492084
Label
Probability Theory : A Comprehensive Course, by Achim Klenke, (electronic resource)
Publication
Note
Description based upon print version of record
Bibliography note
Includes bibliographical references (p. [591]-598) and indexes
Carrier category
online resource
Carrier category code
cr
Content category
text
Content type code
txt
Contents
Basic Measure Theory -- Independence -- Generating Functions -- The Integral -- Moments and Laws of Large Numbers -- Convergence Theorems -- Lp-Spaces and the Radon-Nikodym Theorem -- Conditional Expectations -- Martingales -- Optional Sampling Theorems -- Martingale Convergence Theorems and Their Applications -- Backwards Martingales and Exchangeability -- Convergence of Measures -- Probability Measures on Product Spaces -- Characteristic Functions and the Central Limit Theorem -- Infinitely Divisible Distributions -- Markov Chains -- Convergence of Markov Chains -- Markov Chains and Electrical Networks -- Ergodic Theory -- Brownian Motion -- Law of the Iterated Logarithm -- Large Deviations -- The Poisson Point Process -- The Itô Integral -- Stochastic Differential Equations
Dimensions
unknown
Edition
1st ed. 2008.
Extent
1 online resource (620 p.)
Form of item
online
Isbn
9781848000483
Media category
computer
Media type code
c
Other control number
10.1007/978-1-84800-048-3
Specific material designation
remote
System control number
  • (CKB)1000000000492084
  • (EBL)3062906
  • (SSID)ssj0000319576
  • (PQKBManifestationID)11252066
  • (PQKBTitleCode)TC0000319576
  • (PQKBWorkID)10338645
  • (PQKB)10950712
  • (DE-He213)978-1-84800-048-3
  • (MiAaPQ)EBC3062906
  • (EXLCZ)991000000000492084

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