First Look at Rigorous Probability Theory (Second Edition)



First Look at Rigorous Probability Theory (Second Edition)
World Scientific Publishing Co Pte Ltd | 14-Nov-2006 | ISBN: 9812703705 | 236 pages | File type: PDF | 3.1mb

This textbook is an introduction to probability theory using measure theory. It is designed for graduate students in a variety of fields (mathematics, statistics, economics, management, finance, computer science, and engineering) who require a working knowledge of probability theory that is mathematically precise, but without excessive technicalities. The text provides complete proofs of all the essential introductory results. Nevertheless, the treatment is focused and accessible, with the measure theory and mathematical details presented in terms of intuitive probabilistic concepts, rather than as separate, imposing subjects. In this new edition, many exercises and small additional topics have been added and existing ones expanded. The text strikes an appropriate balance, rigorously developing probability theory while avoiding unnecessary detail.

Contents:

The Need for Measure Theory
Probability Triples
Further Probabilistic Foundations
Expected Values
Inequalities and Convergence
Distributions of Random Variables
Stochastic Processes and Gambling Games
Discrete Markov Chains
More Probability Theorems
Weak Convergence
Characteristic Functions
Decomposition of Probability Laws
Conditional Probability and Expectation
Martingales
General Stochastic Processes


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