PROBABILITY: THEORY, EXAMPLES, PROBLEMS, SIMULATIONS

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A key pedagogical feature of the textbook is the accessible approach to probability concepts through examples with explanations and problems with solutions. The reader is encouraged to simulate in Matlab random experiments and to explore the theoretical aspects of the probabilistic models behind the studied experiments. By this appropriate balance between simulations and rigorous mathematical approach, the reader can experience the excitement of comprehending basic concepts and can develop the intuitive thinking in solving problems. The current textbook does not contain proofs for the stated theorems, but corresponding references are given. Moreover, the given Matlab codes and detailed solutions make the textbook accessible to researchers and undergraduate students, by learning various techniques from probability theory and its applications in other fields. This book is intended not only for students of mathematics but also for students of natural sciences, engineering, computer science and for science researchers, who possess the basic knowledge of calculus for the mathematical concepts of the textbook and elementary programming skills for the Matlab simulations. Sample Chapter(s) Preface Chapter 1: Probability Space Request Inspection Copy Contents: Preface Probability Space Random Variables and Vectors Numerical Characteristics of Random Variables and Vectors Sequences of Random Variables Examples of Stochastic Processes Appendix Bibliography Index Readership: Undergraduate and graduate students, professionals and researchers in mathematics, natural sciences, engineering and computer science areas.

PROBABILITY: THEORY & EXAMPLES (5版)

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書名：Probability: Theory & Examples 5/e 作者：DURRETT 出版社：CAMBRIDGE 出版日期：2019/00/00 ISBN：9781108473682 內容簡介 ●Provides 200 examples and 450 problems to equip readers to build practical intuition and understand the motivation for the theory ●Offers a modern selection of topics, including multidimensional Brownian motion ●The compact style strikes a balance between completeness and readability, covering a great deal of ground in 400 pages 目錄 1. Measure theory 2. Laws of large numbers 3. Central limit theorems 4. Martingales 5. Markov chains 6. Ergodic theorems 7. Brownian motion 8. Applications to random walk 9. Multidimensional Brownian motion Appendix. Measure theory details.