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1. Foundations of Modern Probability (Probability and Its Applications)

Description

The first edition of this single volume on the theory of probability has become a highly-praised standard reference for many areas of probability theory. Chapters from the first edition have been revised and corrected, and this edition contains four new chapters. New material covered includes multivariate and ratio ergodic theorems, shift coupling, Palm distributions, Harris recurrence, invariant measures, and strong and weak ergodicity.

2. Random Measures, Theory and Applications (Probability Theory and Stochastic Modelling)

Description

Offering the first comprehensive treatment of the theory of random measures, this book has a very broad scope, ranging from basic properties of Poisson and related processes to the modern theories of convergence, stationarity, Palm measures, conditioning, and compensation.The three large final chapters focus on applications within the areas ofstochastic geometry, excursion theory, and branching processes. Although this theory plays a fundamental role in most areas of modern probability,much of it, including the most basic material, has previously been availableonly in scores of journal articles. Thebook is primarily directed towards researchers and advanced graduate students instochastic processes and related areas.

3. Foundations of Modern Probability (Probability and Its Applications) by Olav Kallenberg (2010-02-19)

4. Probability Theory: A Comprehensive Course (Universitext)

Description

This second edition of the popular textbook contains a comprehensive course in modern probability theory, covering a wide variety of topics which are not usually found in introductory textbooks, including:
limit theorems for sums of random variables
martingales
percolation
Markov chains and electrical networks
construction of stochastic processes
Poisson point process and infinite divisibility
large deviation principles and statistical physics
Brownian motion
stochastic integral and stochastic differential equations.

The theory is developed rigorously and in a self-contained way, with the chapters on measure theory interlaced with the probabilistic chapters in order to display the power of the abstract concepts in probability theory. This second edition has been carefully extended and includes many new features. It contains updated figures (over 50), computer simulations and some difficult proofs have been made more accessible. A wealth of examples and more than 270 exercises as well as biographic details of key mathematicians support and enliven the presentation. It will be of use to students and researchers in mathematics and statistics in physics, computer science, economics and biology.

5. Foundations of Modern Probability (Probability and Its Applications)

Description

The first edition of this single volume on the theory of probability has become a highly-praised standard reference for many areas of probability theory. Chapters from the first edition have been revised and corrected, and this edition contains four new chapters. New material covered includes multivariate and ratio ergodic theorems, shift coupling, Palm distributions, Harris recurrence, invariant measures, and strong and weak ergodicity.

Conclusion

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