Probability and random processes
著者
書誌事項
Probability and random processes
Clarendon Press , Oxford University Press, 1992
2nd ed
- : pbk
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注記
"Oxford science publications" -- Cover
Bibliography: p. [532]-533
Includes index
内容説明・目次
- 巻冊次
-
: pbk ISBN 9780198536659
内容説明
This successful text has now been comprehensively revised. There are three main aims: to provide a simple but rigorous introduction to probability without exposing the reader to over-much measure theory, to discuss a wide range of random processes in some depth with many examples, and to give the beginner some flavour of more advanced work, by suitable choice of material. The book begins with basic material commonly covered in first-year undergraduate mathematics and statistics courses, and finishes with topics to be found in graduate courses. Important features of this new edition include: new and expanded sections in the early chapters providing more illustrative examples and introducing more ideas early on; two new chapters providing more comprehensive treatment of the simpler properties of martingales and diffusion processes; and more exercises at the ends of almost all sections, with many new problems at the ends of the chapters. The companion volumes Probability and Random Processes: Problems and Solutions (Oxford University Press 1992) includes complete worked solutions to all exercises and problems of this edition.
This book is intended for students at all undergraduate and graduate levels in mathematics and statistics.
目次
- Events and their probabilities
- Random variables and their distributions
- Discrete random variables
- Continuous random variables
- Generating functions and their applications
- Markov chains
- Convergence of random variables
- Random processes
- Stationary processes
- Renewals
- Queues
- Martingales
- Diffusion processes: Appendix I Foundations and notations
- Appendix II Further reading
- Appendix III History and varieties of probability
- Appendix IV John Arbuthnot's Preface to Of the Laws of Chance (1962)
- Bibliography
- List of notation
- Index.
- 巻冊次
-
ISBN 9780198536666
内容説明
This text has three main aims: to provide an introduction to probability without exposing the reader to overmuch measure theory, to discuss a wide range of random processes in some depth with many examples, and to give the beginner some flavour of more advanced work, by suitable choice of material. The book begins with basic material commonly covered in first-year undergraduate mathematics and statistics courses, and finishes with topics to be found in graduate courses. Features of this new edition include: new and expanded sections in the early chapters providing more illustrative examples and introducing more ideas early on; two new chapters providing more comprehensive treatment of the simpler properties of martingales and diffusion processes; and more exercises at the ends of almost all sections, with many new problems at the ends of chapters. The companion volume "Probability and Random Processes: Problems and Solutions" includes complete worked solutions to all exercises and problems of this edition.
The book should be useful as a text for mathematics and natural science undergraduates at all levels from first to final-year degree work and useful as a reference book for graduates and all those interested in the applications of probability theory.
目次
- Events and their probabilities
- random variables and their distributions
- discrete random variables
- continuous random variables
- generating functions and their applications
- Markov chains
- convergence of random variables
- random processes
- stationary processes
- renewals
- queues
- Martingales
- diffusion processes. Appendices: Foundations and notations
- history and varieties of probability
- John Arburthnot's preface to "Of the Laws of Chance" (1692).
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