Integration And Probability

Author: Paul Malliavin
Editor: Springer Science & Business Media
ISBN: 1461242029
Size: 19,59 MB
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An introduction to analysis with the right mix of abstract theories and concrete problems. Starting with general measure theory, the book goes on to treat Borel and Radon measures and introduces the reader to Fourier analysis in Euclidean spaces with a treatment of Sobolev spaces, distributions, and the corresponding Fourier analysis. It continues with a Hilbertian treatment of the basic laws of probability including Doob's martingale convergence theorem and finishes with Malliavin's "stochastic calculus of variations" developed in the context of Gaussian measure spaces. This invaluable contribution gives a taste of the fact that analysis is not a collection of independent theories, but can be treated as a whole.

Measure Integration And Probability

Author: Claude W. Burrill
Editor:
ISBN:
Size: 11,56 MB
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Measure Integral And Probability

Author: Marek Capinski
Editor: Springer Science & Business Media
ISBN: 1447106458
Size: 17,82 MB
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Measure, Integral and Probability is a gentle introduction that makes measure and integration theory accessible to the average third-year undergraduate student. The ideas are developed at an easy pace in a form that is suitable for self-study, with an emphasis on clear explanations and concrete examples rather than abstract theory. For this second edition, the text has been thoroughly revised and expanded. New features include: · a substantial new chapter, featuring a constructive proof of the Radon-Nikodym theorem, an analysis of the structure of Lebesgue-Stieltjes measures, the Hahn-Jordan decomposition, and a brief introduction to martingales · key aspects of financial modelling, including the Black-Scholes formula, discussed briefly from a measure-theoretical perspective to help the reader understand the underlying mathematical framework. In addition, further exercises and examples are provided to encourage the reader to become directly involved with the material.

Exercises And Solutions Manual For Integration And Probability

Author: Gerard Letac
Editor: Springer Science & Business Media
ISBN: 1461242126
Size: 13,20 MB
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This book presents the problems and worked-out solutions for all the exercises in the text by Malliavin. It will be of use not only to mathematics teachers, but also to students using the text for self-study.

Integration Measure And Probability

Author: H. R. Pitt
Editor: Courier Corporation
ISBN: 0486488152
Size: 12,16 MB
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Introductory treatment develops the theory of integration in a general context, making it applicable to other branches of analysis. More specialized topics include convergence theorems and random sequences and functions. 1963 edition.

Measure Theory And Probability Theory

Author: Krishna B. Athreya
Editor: Springer Science & Business Media
ISBN: 038732903X
Size: 17,67 MB
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This is a graduate level textbook on measure theory and probability theory. The book can be used as a text for a two semester sequence of courses in measure theory and probability theory, with an option to include supplemental material on stochastic processes and special topics. It is intended primarily for first year Ph.D. students in mathematics and statistics although mathematically advanced students from engineering and economics would also find the book useful. Prerequisites are kept to the minimal level of an understanding of basic real analysis concepts such as limits, continuity, differentiability, Riemann integration, and convergence of sequences and series. A review of this material is included in the appendix. The book starts with an informal introduction that provides some heuristics into the abstract concepts of measure and integration theory, which are then rigorously developed. The first part of the book can be used for a standard real analysis course for both mathematics and statistics Ph.D. students as it provides full coverage of topics such as the construction of Lebesgue-Stieltjes measures on real line and Euclidean spaces, the basic convergence theorems, L^p spaces, signed measures, Radon-Nikodym theorem, Lebesgue's decomposition theorem and the fundamental theorem of Lebesgue integration on R, product spaces and product measures, and Fubini-Tonelli theorems. It also provides an elementary introduction to Banach and Hilbert spaces, convolutions, Fourier series and Fourier and Plancherel transforms. Thus part I would be particularly useful for students in a typical Statistics Ph.D. program if a separate course on real analysis is not a standard requirement. Part II (chapters 6-13) provides full coverage of standard graduate level probability theory. It starts with Kolmogorov's probability model and Kolmogorov's existence theorem. It then treats thoroughly the laws of large numbers including renewal theory and ergodic theorems with applications and then weak convergence of probability distributions, characteristic functions, the Levy-Cramer continuity theorem and the central limit theorem as well as stable laws. It ends with conditional expectations and conditional probability, and an introduction to the theory of discrete time martingales. Part III (chapters 14-18) provides a modest coverage of discrete time Markov chains with countable and general state spaces, MCMC, continuous time discrete space jump Markov processes, Brownian motion, mixing sequences, bootstrap methods, and branching processes. It could be used for a topics/seminar course or as an introduction to stochastic processes. Krishna B. Athreya is a professor at the departments of mathematics and statistics and a Distinguished Professor in the College of Liberal Arts and Sciences at the Iowa State University. He has been a faculty member at University of Wisconsin, Madison; Indian Institute of Science, Bangalore; Cornell University; and has held visiting appointments in Scandinavia and Australia. He is a fellow of the Institute of Mathematical Statistics USA; a fellow of the Indian Academy of Sciences, Bangalore; an elected member of the International Statistical Institute; and serves on the editorial board of several journals in probability and statistics. Soumendra N. Lahiri is a professor at the department of statistics at the Iowa State University. He is a fellow of the Institute of Mathematical Statistics, a fellow of the American Statistical Association, and an elected member of the International Statistical Institute.

Proceedings Of The Fourth Berkeley Symposium On Mathematical Statistics And Probability

Author:
Editor: Univ of California Press
ISBN:
Size: 15,15 MB
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Inequalities In Statistics And Probability

Author: Yung Liang Tong
Editor: IMS
ISBN: 9780940600041
Size: 18,23 MB
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Proceedings Of The Berkeley Symposium On Mathematical Statistics And Probability

Author: Jerzy Neyman
Editor:
ISBN:
Size: 13,68 MB
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Functional Integration And Partial Differential Equations

Author: Mark Iosifovich Freĭdlin
Editor: Princeton University Press
ISBN: 9780691083629
Size: 13,92 MB
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This book considers problems arising the theory of differential equations. This book is not only intended for mathematicians specializing in the theory of differential equations or in probability theory but also for specialists in asymptotic methods and functional analysis.