A course in probability theory /

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Detalles Bibliográficos
Clasificación:Libro Electrónico
Autor principal: Chung, Kai Lai, 1917-2009
Formato: Electrónico eBook
Idioma:Inglés
Publicado: San Diego : Academic Press, ©2001.
Edición:3rd ed.
Temas:
Probabilities.
Probabilités.
probability.
MATHEMATICS > Probability & Statistics > General.
Acceso en línea:Texto completo
Tabla de Contenidos:
  • Cover
  • Title Page
  • Copyright Page
  • Contents
  • Preface to the third edition
  • Preface to the second edition
  • Preface to the first edition
  • Chapter 1. Distribution function
  • 1.1 Monotone functions
  • 1.2 Distribution functions
  • 1.3 Absolutely continuous and singular distributions
  • Chapter 2. Measure theory
  • 2.1 Classes of sets
  • 2.2 Probability measures and their distribution functions
  • Chapter 3. Random variable. Expectation. Independence
  • 3.1 General definitions
  • 3.2 Properties of mathematical expectation
  • 3.3 Independence
  • Chapter 4. Convergence concepts
  • 4.1 Various modes of convergence
  • 4.2 Almost sure convergence; Borel-Cantelli lemma
  • 4.3 Vague convergence
  • 4.4 Continuation
  • 4.5 Uniform integrability; convergence of moments
  • Chapter 5. Law of large numbers. Random series
  • 5.1 Simple limit theorems
  • 5.2 Weak law of large numbers
  • 5.3 Convergence of series
  • 5.4 Strong law of large numbers
  • 5.5 Applications
  • Bibliographical Note
  • Chapter 6. Characteristic function
  • 6.1 General properties; convolutions
  • 6.2 Uniqueness and inversion
  • 6.3 Convergence theorems
  • 6.4 Simple applications
  • 6.5 Representation theorems
  • 6.6 Multidimensional case; Laplace transforms
  • Bibliographical Note
  • Chapter 7. Central limit theorem and its ramifications
  • 7.1 Liapounov's theorem
  • 7.2 Lindeberg-Feller theorem
  • 7.3 Ramifications of the central limit theorem
  • 7.4 Error estimation
  • 7.5 Law of the iterated logarithm
  • 7.6 Infinite divisibility
  • Bibliographical Note
  • Chapter 8. Random walk
  • 8.1 Zero-or-one laws
  • 8.2 Basic notions
  • 8.3 Recurrence
  • 8.4 Fine structure
  • 8.5 Continuation
  • Bibliographical Note
  • Chapter 9. Conditioning. Markov property. Martingale
  • 9.1 Basic properties of conditional expectation
  • 9.2 Conditional independence; Markov property
  • 9.3 Basic properties of smartingales
  • 9.4 Inequalities and convergence
  • 9.5 Applications
  • Bibliographical Note
  • Supplement: Measure and Integral
  • 1 Construction of measure
  • 2 Characterization of extensions
  • 3 Measures in R
  • 4 Integral
  • 5 Applications
  • General Bibliography
  • Index
  • Last Page

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