An introduction to Measure - Theoretic Probability

George G. Roussas

444 pages, parution le 26/11/2004

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Résumé

This book provides in a concise, yet detailed way, the bulk of the probabilistic tools that a student working toward an advanced degree in statistics, probability and other related areas, should be equipped with. The approach is classical, avoiding the use of mathematical tools not necessary for carrying out the discussions. All proofs are presented in full detail.

Audience :
Graduate students primarily in statistics, mathematics, electrical & computer engineering or other information sciences; mathematical economics/finance in departments of economics.

Sommaire

Certain Classes of Sets, Measurability, Pointwise Approximation
Definition and Construction of a Measure and Its Basic Properties
Some Modes of Convergence of a Sequence of Random Variables and Their Relationships
The Integral of a Random Variable and Its Basic Properties
Standard Convergence Theorems, The Fubini Theorem
Standard Moment and Probability Inequalities, Convergence in the r-th Mean and Its Implications
The Hahn-Jordan Decomposition Theorem, The Lebesgue Decomposition Theorem, and The Radon-Nikcodym Theorem
Distribution Functions and Their Basic Properties, Helly-Bray Type Results
Conditional Expectation and Conditional Probability, and Related Properties and Results
Independence
Topics from the Theory of Characteristic Functions
The Central Limit Problem: The Centered Case
The Central Limit Problem: The Noncentered Case
Topics from Sequences of Independent Random Variables
Topics from Ergodic Theory

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Caractéristiques techniques

	PAPIER
Éditeur(s)	Elsevier
Auteur(s)	George G. Roussas
Parution	26/11/2004
Nb. de pages	444
Format	15,5 x 23,5
Couverture	Relié
Poids	840g
Intérieur	Noir et Blanc
EAN13	9780125990226
ISBN13	978-0-12-599022-6