Probability Theory: An Advanced Course / Edition 1

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Overview

This book is an advanced text on probability theory. By presupposing the background of a standard first course in real analysis and a 'soft' course in probability theory, it gives a compact treatment of several key topics in probability, selected on the basis of their importance in forming the foundations of the modern theory of shastic processes. It is ideal for graduate students and researchers in probability theory and shastic processes and their applications. It is also well suited for scientists in allied fields such as mathematical statistics/ economics/physics, electrical engineering, operations research who wish to augment their background in probability theory.

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Product Details

  • ISBN-13: 9780387945583
  • Publisher: Springer New York
  • Publication date: 10/28/1995
  • Series: Universitext Series
  • Edition description: Softcover reprint of the original 1st ed. 1995
  • Edition number: 1
  • Pages: 138
  • Product dimensions: 9.21 (w) x 6.14 (h) x 0.33 (d)

Table of Contents

1 Introduction.- 1.1 Random Variables.- 1.2 Monotone Class Theorems.- 1.3 Expectations and Uniform Integrability.- 1.4 Independence.- 1.5 Convergence Concepts.- 1.6 Additional Exercises.- 2 Spaces of Probability Measures.- 2.1 The Prohorov Topology.- 2.2 Skorohod’s Theorem.- 2.3 Compactness in P(S).- 2.4 Complete Metrics on P(S).- 2.5 Characteristic Functions.- 2.6 Additional Exercises.- 3 Conditioning and Martingales.- 3.1 Conditional Expectations.- 3.2 Martingales.- 3.3 Convergence Theorems.- 3.4 Martingale Inequalities.- 3.5 Additional Exercises.- 4 Basic Limit Theorems.- 4.1 Introduction.- 4.2 Strong Law of Large Numbers.- 4.3 Central Limit Theorem.- 4.4 The Law of Iterated Logarithms.- 4.5 Large Deviations.- 4.6 Tests for Convergence.- 4.7 Additional Exercises.- 5 Markov Chains.- 5.1 Construction and the Strong Markov Property.- 5.2 Classification of States.- 5.3 Stationary Distributions.- 5.4 Transient and Null Recurrent Chains.- 5.5 Additional Exercises.- 6 Foundations of Continuous-Time Processes.- 6.1 Introduction.- 6.2 Separability and Measurability.- 6.3 Continuous Versions.- 6.4 Cadlag Versions.- 6.5 Examples of Shastic Processes.- 6.6 Additional Exercises.- References.

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  • Anonymous

    Posted August 31, 2004

    A must for students in Advanced Statistical Theory

    This book is good for those who need to learn Measure theoretic approach to probablity theory. This book requires a prior course on Measure theory. Measure theoretic approach provides an axiomatic, rigorous formulation to basic probablity theory as well as a unified view of stochastic processes(discrete and continuous time). This is a good book for mathematically inclined people.

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