Probability: Theory and Examples / Edition 2

Probability: Theory and Examples / Edition 2

by Richard Durrett
     
 

ISBN-10: 0534243185

ISBN-13: 9780534243180

Pub. Date: 09/28/1995

Publisher: Cengage Learning


Modern and measure-theory based, this text is intended primarily for the first-year graduate course in probability theory.

Overview


Modern and measure-theory based, this text is intended primarily for the first-year graduate course in probability theory.

Product Details

ISBN-13:
9780534243180
Publisher:
Cengage Learning
Publication date:
09/28/1995
Edition description:
Older Edition
Pages:
528
Product dimensions:
6.61(w) x 9.57(h) x 1.01(d)

Related Subjects

Table of Contents


INTRODUCTORY LECTURE 1. LAWS OF LARGE NUMBERS Basic Definitions / Random Variables / Expected Value / Independence / Weak Laws of Large Numbers / Borel-Cantelli Lemmas / Strong Laws of Large Numbers / Convergence of Random Series / Large Deviations 2. CENTRAL LIMIT THEOREMS The De Moivre-Laplace Theorem / Weak Convergence / Characteristic Functions / Central Limit Theorems / Local Limit Theorems / Poisson Convergence / Stable Laws / Infinitely Divisible Distributions / Limit Theorems in R^d 3. RANDOM WALKS Stopping Times / Recurrence / Visits to 0, Arcsine Laws / Renewal Theory 4. MARTINGALES Conditional Expectation / Martingales, Almost Sure Convergence / Examples / Doob''''s Inequality / L^p Convergence / Uniform Integrability, Convergence in L^1 / Backwards Martingales / Optional Stopping Theorems 5. MARKOV CHAINS Definitions and Examples / Extensions of the Markov Property / Recurrence and Transience / Stationary Measures / Asymptotic Behavior / General State Space 6. ERGODIC THEOREMS Definitions and Examples / Birkhoff''''s Ergodic Theorem / Recurrence / Mixing / Entropy / A Subadditive Ergodic Theorem / Applications 7. BROWNIAN MOTION Definition and Construction / Markov Property, Blumenthal''''s 0-1 Law / Stopping Times, Strong Markov Property / Maxima and Zeros / Martingales / Donsker''''s Theorem / CLT''''s for Dependent Variables / Empirical Distributions, Brownian Bridge / Laws of the Iterated Logarithm / APPENDIX: MEASURE THEORY / Lebesgue-Stieljes Measures / Caratheodary''''s Extension Theorem / Completion, etc. / Integration / Properties of the Integral / Product Measures, Fubini''''s Theorem / Kolmogorov''''s Extension Theorem / Radon-Nikodym Theorem / Differentiating Under the Integral / REFERENCES / NOTATION / NORMAL TABLE / INDEX

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