A Modern Approach to Probability Theory - Rilegato

Fristedt, Bert; Gray, Lawrence

Rilegato

ISBN 10: 0817638075 ISBN 13: 9780817638078

Casa editrice: Birkhauser, 1996

Riassunto

Students and teachers of mathematics and related fields will find this book a comprehensive and modern approach to probability theory, providing the background and techniques to go from the beginning graduate level to the point of specialization in research areas of current interest. The book is designed for a two- or three-semester course, assuming only courses in undergraduate real analysis or rigorous advanced calculus, and some elementary linear algebra. A variety of applications—Bayesian statistics, financial mathematics, information theory, tomography, and signal processing—appear as threads to both enhance the understanding of the relevant mathematics and motivate students whose main interests are outside of pure areas.

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Recensione

"Covers the essentials in a clear and readable fashion... A must for professionals and an attractive text for a graduate course."   ―American Mathematical Monthly  (review of the first edition)

"This ambitious book is intended as ‘a textbook in probability for graduate students in mathematics and related areas such as economics, statistics, physics and operations research’...The coverage is careful and thorough...Quite a lot of fairly recent material is incorporated, and this is certainly one of the book’s strengths. The selection of material is sensible, and the quality of exposition is good...In sum: the book contains a lot of good mathematics, nicely done, and should prove useful to students and teachers, and to specialists in probability theory."   ―Mathematical Reviews (review of the first edition)

"The book takes the reader from a relatively low level.... To the point where he or she can specialize in research topics of current interest. ...an outstanding basis for teaching a graduate course in probability theory. The exhaustive compilation of results and detailed index also make it a very useful reference text for the more advanced probabilist... a good buy for anyone looking for a very accessible and complete mathematical account of modern probability theory."   ―Journal of the American Statistical Association  (review of the first edition)

Contenuti

List of Tables * Preface * Part I: Probability Spaces, Random Variables, and Expectations * Probability Spaces * Random Variables * Distribution Functions * Expectations: Theory * Expectations: Applications * Calculating Probabilities and Measures * Measure Theory: Existence and Uniqueness * Integration Theory * Part 2: Independence and Sums * Stochastic Independence * Sums of Independent Random Variables * Random Walk * Theorems of A.S. Convergence * Characteristic Functions * Part 3: Convergence in Distribution * Convergence in Distribution on the Real Line * Distributional Limit Theorems for Partial Sums * Infinitely Divisible and Stable Distributions as Limits * Convergence in Distribution on Polish Spaces * The Invariance Principle and Brownian Motion * Part 4: Conditioning * Spaces of Random Variables * Conditional Probabilities * Construction of Random Sequences * Conditional Expectations * Part 5: Random Sequences * Martingales * Renewal Sequences * Time-homogeneous Markov Sequences * Exchangeable Sequences * Stationary Sequences * Part 6: Stochastic Processes * Point Processes * Diffusions and Stochastic Calculus * Applications of Stochastic Calculus * Part 7: Appendices * Appendix A. Notation and Usage of Terms * Appendix B. Metric Spaces * Appendix C. Topological Spaces * Appendix D. Riemann–Stieltjes Integration * Appendix E. Taylor Approximations, C-Valued Logarithms * Appendix F. Bibliography * Appendix G. Comments and Credits * Index

Dettagli dell?edizione

• Editore: Birkhauser
• Data di pubblicazione: 1996
• ISBN 10: 0817638075
• ISBN 13: 9780817638078
• Rilegatura: Copertina rigida
• Lingua: Inglese
• Numero di pagine: 756