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Dispatched from the UK in 4 business days When will my order arrive? Haim Brezis. Serge Lang. Loring W. Vladimir I. Vladimir A. Jean Jacod. Joseph J. Achim Klenke. Fernando Q. Manfredo P. Do Carmo. Saunders MacLane. Ferdinand Verhulst. Eberhard Freitag. Martin Arkowitz. Dirk Van Dalen. Clara Loeh. Benjamin Steinberg.
Home Contact us Help Free delivery worldwide. Free delivery worldwide. Bestselling Series. Harry Potter. Popular Features. Home Learning. Probability Essentials. Description This introduction can be used, at the beginning graduate level, for a one-semester course on probability theory or for self-direction without benefit of a formal course; the measure theory needed is developed in the text.
It will also be useful for students and teachers in related areas such as finance theory, electrical engineering, and operations research. The text covers the essentials in a directed and lean way with 28 short chapters, and assumes only an undergraduate background in mathematics. Readers are taken right up to a knowledge of the basics of Martingale Theory, and the interested student will be ready to continue with the study of more advanced topics, such as Brownian Motion and Ito Calculus, or Statistical Inference.
Product details Format Paperback pages Dimensions x x Illustrations note X, p. Other books in this series. Add to basket. Algebra Serge Lang. An Introduction to Manifolds Loring W. Ordinary Differential Equations Vladimir I. Mathematical Analysis I Vladimir A. Probability Essentials Jean Jacod. Probability Theory Achim Klenke. Differential Forms and Applications Manfredo P.
Complex Analysis Eberhard Freitag. Introduction to Homotopy Theory Martin Arkowitz. Logic and Structure Dirk Van Dalen. Geometric Group Theory Clara Loeh. Table of contents 1. Introduction 2. Axioms of Probability 3. Conditional Probability and Independence 4. Probabilities on a Countable Space 5. Random Variables on a Countable Space 6. Construction of a Probability Measure 7. Construction of a Probability Measure on R 8. Random Variables 9. Integration with Respect to a Probability Measure Independent Random Variables Probability Distributions on R Probability Distributions on Rn Characteristic Functions Properties of Characteristic Functions Sums of Independent Random Variables Convergence of Random Variables Weak Convergence Weak Convergence and Characteristic Functions The Laws of Large Numbers The Central Limit Theorem L2 and Hilbert Spaces Conditional Expectation Martingales Supermartingales and Submartingales Martingale Inequalities Martingales Convergence Theorems The Radon-Nikodym Theorem show more.
Review quote " The book is a lean and largely self-contained introduction to the modern theory of probability, aimed at advanced undergraduate or beginning graduate students. The 28 short chapters belie the book's genesis as polished lecture notes; the exposition is sleek and rigorous and each chapter ends with a supporting collection of mainly routine exercises.
The authors make it clear what luggage is required for this exhilarating trek, With this understood, the itinerary is immaculately paced and planned with just the right balances of technical ascents and pauses to admire the scenery. Within the constraints of a slim volume, it is hard to imagine how the authors could have done a more effective or more attractive job.
The topics are treated in a mathematically and pedagogically digestible way. The writing is concise and crisp: the average chapter length is about eight pages. Numerous exercises add to the value of the text as a teaching tool.
In conclusion, this is an excellent text for the intended audience. Rating details. Book ratings by Goodreads. Goodreads is the world's largest site for readers with over 50 million reviews. We're featuring millions of their reader ratings on our book pages to help you find your new favourite book. Close X. Learn about new offers and get more deals by joining our newsletter.
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It seems that you're in Germany. We have a dedicated site for Germany. Authors: Jacod , Jean, Protter , Philip. We have made small changes throughout the book, including the exercises, and we have tried to correct if not all, then at least most of the typos. We wish to thank the many colleagues and students who have commented c- structively on the book since its publication two years ago, and in particular Professors Valentin Petrov, Esko Valkeila, Volker Priebe, and Frank Knight. These corrections have improved the book in subtle yet important ways, and the authors are most grateful to him. We also treat measure theory and Lebesgue integration, concentrating on those aspects which are especially germane to the study of Probability Theory.