Analysis And Probability
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| Author | : Aurel Spataru |
| Publisher | : Newnes |
| Total Pages | : 459 |
| Release | : 2013-01-12 |
| Genre | : Mathematics |
| ISBN | : 0124017274 |
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.
| Author | : Robert B. Ash |
| Publisher | : Academic Press |
| Total Pages | : 495 |
| Release | : 2014-07-03 |
| Genre | : Mathematics |
| ISBN | : 1483191427 |
Real Analysis and Probability provides the background in real analysis needed for the study of probability. Topics covered range from measure and integration theory to functional analysis and basic concepts of probability. The interplay between measure theory and topology is also discussed, along with conditional probability and expectation, the central limit theorem, and strong laws of large numbers with respect to martingale theory. Comprised of eight chapters, this volume begins with an overview of the basic concepts of the theory of measure and integration, followed by a presentation of various applications of the basic integration theory. The reader is then introduced to functional analysis, with emphasis on structures that can be defined on vector spaces. Subsequent chapters focus on the connection between measure theory and topology; basic concepts of probability; and conditional probability and expectation. Strong laws of large numbers are also examined, first from the classical viewpoint, and then via martingale theory. The final chapter is devoted to the one-dimensional central limit problem, paying particular attention to the fundamental role of Prokhorov's weak compactness theorem. This book is intended primarily for students taking a graduate course in probability.
| Author | : R. M. Dudley |
| Publisher | : Cambridge University Press |
| Total Pages | : 570 |
| Release | : 2002-10-14 |
| Genre | : Mathematics |
| ISBN | : 9780521007542 |
This classic text offers a clear exposition of modern probability theory.
| Author | : Igor Rychlik |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 287 |
| Release | : 2006-10-07 |
| Genre | : Mathematics |
| ISBN | : 3540395210 |
This text presents notions and ideas at the foundations of a statistical treatment of risks. The focus is on statistical applications within the field of engineering risk and safety analysis. Coverage includes Bayesian methods. Such knowledge facilitates the understanding of the influence of random phenomena and gives a deeper understanding of the role of probability in risk analysis. The text is written for students who have studied elementary undergraduate courses in engineering mathematics, perhaps including a minor course in statistics. This book differs from typical textbooks in its verbal approach to many explanations and examples.
| Author | : Richard F. Bass |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 408 |
| Release | : 1994-12-16 |
| Genre | : Mathematics |
| ISBN | : 0387943870 |
In recent years, there has been an upsurge of interest in using techniques drawn from probability to tackle problems in analysis. These applications arise in subjects such as potential theory, harmonic analysis, singular integrals, and the study of analytic functions. This book presents a modern survey of these methods at the level of a beginning Ph.D. student. Highlights of this book include the construction of the Martin boundary, probabilistic proofs of the boundary Harnack principle, Dahlberg's theorem, a probabilistic proof of Riesz' theorem on the Hilbert transform, and Makarov's theorems on the support of harmonic measure. The author assumes that a reader has some background in basic real analysis, but the book includes proofs of all the results from probability theory and advanced analysis required. Each chapter concludes with exercises ranging from the routine to the difficult. In addition, there are included discussions of open problems and further avenues of research.
| Author | : Edward Nelson |
| Publisher | : Princeton University Press |
| Total Pages | : 112 |
| Release | : 1987 |
| Genre | : Mathematics |
| ISBN | : 9780691084749 |
Using only the very elementary framework of finite probability spaces, this book treats a number of topics in the modern theory of stochastic processes. This is made possible by using a small amount of Abraham Robinson's nonstandard analysis and not attempting to convert the results into conventional form.
| Author | : Palle E. T. Jorgensen |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 320 |
| Release | : 2007-10-17 |
| Genre | : Mathematics |
| ISBN | : 0387330828 |
Combines analysis and tools from probability, harmonic analysis, operator theory, and engineering (signal/image processing) Interdisciplinary focus with hands-on approach, generous motivation and new pedagogical techniques Numerous exercises reinforce fundamental concepts and hone computational skills Separate sections explain engineering terms to mathematicians and operator theory to engineers Fills a gap in the literature
| Author | : Saloman Bochner |
| Publisher | : Univ of California Press |
| Total Pages | : 184 |
| Release | : 2023-11-15 |
| Genre | : Mathematics |
| ISBN | : 0520345290 |
This title is part of UC Press's Voices Revived program, which commemorates University of California Press’s mission to seek out and cultivate the brightest minds and give them voice, reach, and impact. Drawing on a backlist dating to 1893, Voices Revived makes high-quality, peer-reviewed scholarship accessible once again using print-on-demand technology. This title was originally published in 1955.
| Author | : R. M. Dudley |
| Publisher | : CRC Press |
| Total Pages | : 479 |
| Release | : 2018-02-01 |
| Genre | : Mathematics |
| ISBN | : 1351093096 |
Written by one of the best-known probabilists in the world this text offers a clear and modern presentation of modern probability theory and an exposition of the interplay between the properties of metric spaces and those of probability measures. This text is the first at this level to include discussions of the subadditive ergodic theorems, metrics for convergence in laws and the Borel isomorphism theory. The proofs for the theorems are consistently brief and clear and each chapter concludes with a set of historical notes and references. This book should be of interest to students taking degree courses in real analysis and/or probability theory.
| Author | : Gary L. Wise |
| Publisher | : Oxford University Press |
| Total Pages | : 224 |
| Release | : 1993-10-07 |
| Genre | : Mathematics |
| ISBN | : 019536130X |
A counterexample is any example or result that is the opposite of one's intuition or to commonly held beliefs. Counterexamples can have great educational value in illuminating complex topics that are difficult to explain in a rigidly logical, written presentation. For example, ideas in mathematical sciences that might seem intuitively obvious may be proved incorrect with the use of a counterexample. This monograph concentrates on counterexamples for use at the intersection of probability and real analysis, which makes it unique among such treatments. The authors argue convincingly that probability theory cannot be separated from real analysis, and this book contains over 300 examples related to both the theory and application of mathematics. Many of the examples in this collection are new, and many old ones, previously buried in the literature, are now accessible for the first time. In contrast to several other collections, all of the examples in this book are completely self-contained--no details are passed off to obscure outside references. Students and theorists across fields as diverse as real analysis, probability, statistics, and engineering will want a copy of this book.
