Probability and random processes
著者
書誌事項
Probability and random processes
（Texts from Oxford University Press）
Oxford University Press, c2001
3rd ed
- : hbk
- : pbk
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注記
1st ed. 1982, 2nd ed. 1992, 3rd ed. 2001, reprinted 2002, 2003 (twice), 2004 (with corrections), 2005 (twice), 2006, 2007, 2008
Includes bibliographical references (p. [580]-582) and index
内容説明・目次
- 巻冊次
-
: pbk ISBN 9780198572220
内容説明
The third edition of this successful text gives a rigorous introduction to probability theory and the discussion of the most important random processes in some depth. It includes various topics which are suitable for undergraduate courses, but are not routinely taught. It is suitable to the beginner, and provides a taste and encouragement for more advanced work. There are four main aims: 1) to provide a thorough but straightforward account of basic probability,
giving the reader a natural feel for the subject unburdened by oppressive technicalities, 2) to discuss important random processes in depth with many examples. 3) to cover a range of important but less routine topics, 4) to impart to the beginner the flavour of more advanced work. The books begins with
basic ideas common to many undergraduate courses in mathematics, statistics and the sciences; in concludes with topics usually found at graduate level. The ordering and numbering of material in this third edition has been mostly preserved from the second. Minor alterations and additions have been added for clearer exposition. Highlights include new sections on sampling and Markov chain Monte Carlo, geometric probability, coupling and Poisson approximation, large deviations, spatial Poisson
processes, renewal-reward, queueing networks, stochastic calculus, Ito's formula and option pricing in the Black-Scholes model for financial markets. In addition there are many (nearly 400) new exercises and problems that are entertaining and instructive; their solutions can be found in the companion
volume 'One Thousand Exercises in Probability', (OUP 2001).
目次
- 1. Events and their probabilities
- 2. Random variables and their distribution
- 3. Discrete random variables
- 4. Continuous random variables
- 5. Generating functions and their applications
- 6. Markov chains
- 7. Convergence of random variables
- 8. Random processes
- 9. Stationary processes
- 10. Renewals
- 11. Queues
- 12. Martingales
- 13. Diffusion processes
- Appendices
- Bibliography
- List of notation
- Index
- 巻冊次
-
: hbk ISBN 9780198572237
内容説明
The third edition of this text gives a rigorous introduction to probability theory and the discussion of the most important random processes in some depth. It includes various topics which are suitable for undergraduate courses, but are not routinely taught. It is suitable to the beginner, and should provide a taste and encouragement for more advanced work.There are four main aims: 1) to provide a thorough but straightforward account of basic probability, giving the reader a natural feel for the subject unburdened by oppressive technicalities, 2) to discuss important random processes in depth with many examples. 3) to cover a range of important but less routine topics, 4) to impart to the beginner the flavour of more advanced work. The books begins with basic ideas common to many undergraduate courses in mathematics, statistics and the sciences; in concludes with topics usually found at graduate level. The ordering and numbering of material in this third edition has been mostly preserved from the second. Minor alterations and additions have been added for clearer exposition.
目次
- Events and their probabilities
- random variables and their distribution
- 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.
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