Title:
A course in probability theory / Kai Lai Chung.
Main Entry:
Chung, Kai Lai 1917-2009.
Publisher:
Academic Press,
Publication Date:
�2001.
Publication Place:
San Diego :
ISBN:
0121741516
9780121741518
Subject:
Probabilities.
Probabilities.
Wahrscheinlichkeitstheorie
Einf�uhrung
Probabilities.
Wahrscheinlichkeitstheorie.
Probabilidades.
Einfuhrung.
Edition:
3rd ed.
Contents:
Distribution function -- Monotone functions Distribution functions Absolutely continuous and singular distributions Measure theory -- Classes of sets Probability measures and their distribution functions Random variable: Expectation: Independence -- General definitions Properties of mathematical expectation Independence Convergence concepts -- Various modes of convergence Almost sure convergence; Borel-Cantelli lemma Vague convergence Continuation Uniform integrability; convergence of moments Law of large numbers: Random series -- Simple limit theorems Weak law of large numbers Convergence of series Strong law of large numbers Applications Characteristic function -- General properties; convolutions Uniqueness and inversion Convergence theorems Simple applications Representation theorems Multidimensional case; Laplace transforms Central limit theorem and its ramifications -- Liapounov's theorem Lindeberg-Feller theorem Ramifications of the central limit theorem Error estimation Law of the iterated logarithm Infinite divisibility Random walk -- Zero-or-one laws Basic notions Recurrence Fine structure Continuation Conditioning: Markov property: Martingale -- Basic properties of conditional expectation Conditional independence; Markov property Basic properties of smartingales Inequalities and convergence Applications Supplement: Measure and Integral -- Construction of measure Characterization of extensions Measures in R Integral Applications
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