Analysis and Probability

ISBN-13: 9780124016651 / Angielski / Twarda / 2013 / 404 str.

Aurel Spataru

Opis

Probability theory is a rapidly expanding field and is used in many areas of science and technology. Beginning from a basis of abstract analysis, this mathematics book develops the knowledge needed for advanced students to develop a complex understanding of probability. The first part of the book systematically presents concepts and results from analysis before embarking on the study of probability theory. The initial section will also be useful for those interested in topology, measure theory, real analysis and functional analysis. The second part of the book presents the concepts, methodology and fundamental results of probability theory. Exercises are included throughout the text, not just at the end, to teach each concept fully as it is explained, including presentations of interesting extensions of the theory. The complete and detailed nature of the book makes it ideal as a reference book or for self-study in probability and related fields.

• Covers a wide range of subjects including f-expansions, Fuk-Nagaev inequalities and Markov triples.
• Provides multiple clearly worked exercises with complete proofs.
• Guides readers through examples so they can understand and write research papers independently.

Recenzje

"...The subject of this book is modern probability theory and it gives a full self-contained presentation of fundamental results within the area.it presents the theory of probability from a measure-theoretic point of view." --MathSciNet, Analysis and Probability

"This monograph is a self-contained and compactly written text book on probability theory for graduate students.the textbook gives a rigorous.presentation of the fundamental results in probability theory with an emphasis on the interaction between analysis and probability." --Zentralblatt MATH, 1278.60002

"Spataru presents a probability theory text for graduate students who have a solid background in abstract analysis, which is required because he develops probability theory from a measure-theoretic perspective." --Reference & Research Book News, October 2013

Spis treści

Chapter 1: Elements of Set TheoryChapter 2: Topological PreliminariesChapter 3: Measure SpacesChapter 4: The IntegralChapter 5: Measures on Product -algebrasChapter 6: Elementary Notions in Probability TheoryChapter 7: Distribution Functions and Characteristic FunctionsChapter 8: Probabilities on Metric SpacesChapter 9: Central Limit ProblemChapter 10: Sums of Independent Random VariablesChapter 11: ConditioningChapter 12: Ergodicity, Mixing and Stationarity