Probability Theory An Analytic View

Author : Daniel W. Stroock
Publisher : Cambridge University Press
Page : 550 pages
File Size : 41,9 Mb
Release : 2010-12-31
Category : Mathematics
ISBN : 9781139494618

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Probability Theory by Daniel W. Stroock Pdf

This second edition of Daniel W. Stroock's text is suitable for first-year graduate students with a good grasp of introductory, undergraduate probability theory and a sound grounding in analysis. It is intended to provide readers with an introduction to probability theory and the analytic ideas and tools on which the modern theory relies. It includes more than 750 exercises. Much of the content has undergone significant revision. In particular, the treatment of Levy processes has been rewritten, and a detailed account of Gaussian measures on a Banach space is given.

Author : Daniel W. Stroock
Publisher : Unknown
Page : 512 pages
File Size : 49,8 Mb
Release : 1993
Category : Probabilities
ISBN : OCLC:1176440103

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Probability Theory: an Analytic View by Daniel W. Stroock Pdf

This section also explores the connection between martingales and various aspects of classical analysis, and the connections between Wiener's measure and classical potential theory. Although the book is primarily intended for students and practitioners of probability theory and analysis, it will also be a valuable reference for those in fields as diverse as physics, engineering, and economics.

Author : Daniel W. Stroock
Publisher : Cambridge University Press
Page : 558 pages
File Size : 50,9 Mb
Release : 1999
Category : Mathematics
ISBN : 0521663490

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Probability Theory, an Analytic View by Daniel W. Stroock Pdf

This revised edition is suitable for a first-year graduate course on probability theory. It is intended for students with a good grasp of introductory, undergraduate probability and is a reasonably sophisticated introduction to modern analysis for those who want to learn what these two topics have to say about each other. The first part of the book deals with independent random variables, Central Limit phenomena, the general theory of weak convergence and several of its applications, as well as elements of both the Gaussian and Markovian theory of measures on function space. The introduction of conditional expectation values is postponed until the second part of the book where it is applied to the study of martingales. This section also explores the connection between martingales and various aspects of classical analysis and the connections between Wiener's measure and classical potential theory.

Author : Daniel Dugue,E. Lukacs,V. K. Rohatgi
Publisher : Springer
Page : 197 pages
File Size : 55,8 Mb
Release : 2006-11-14
Category : Mathematics
ISBN : 9783540367857

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Analytical Methods in Probability Theory by Daniel Dugue,E. Lukacs,V. K. Rohatgi Pdf

Author : Daniel W. Stroock
Publisher : Princeton University Press
Page : 288 pages
File Size : 43,6 Mb
Release : 2003-05-26
Category : Mathematics
ISBN : 9780691115436

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Markov Processes from K. Itô's Perspective by Daniel W. Stroock Pdf

Kiyosi Itô's greatest contribution to probability theory may be his introduction of stochastic differential equations to explain the Kolmogorov-Feller theory of Markov processes. Starting with the geometric ideas that guided him, this book gives an account of Itô's program. The modern theory of Markov processes was initiated by A. N. Kolmogorov. However, Kolmogorov's approach was too analytic to reveal the probabilistic foundations on which it rests. In particular, it hides the central role played by the simplest Markov processes: those with independent, identically distributed increments. To remedy this defect, Itô interpreted Kolmogorov's famous forward equation as an equation that describes the integral curve of a vector field on the space of probability measures. Thus, in order to show how Itô's thinking leads to his theory of stochastic integral equations, Stroock begins with an account of integral curves on the space of probability measures and then arrives at stochastic integral equations when he moves to a pathspace setting. In the first half of the book, everything is done in the context of general independent increment processes and without explicit use of Itô's stochastic integral calculus. In the second half, the author provides a systematic development of Itô's theory of stochastic integration: first for Brownian motion and then for continuous martingales. The final chapter presents Stratonovich's variation on Itô's theme and ends with an application to the characterization of the paths on which a diffusion is supported. The book should be accessible to readers who have mastered the essentials of modern probability theory and should provide such readers with a reasonably thorough introduction to continuous-time, stochastic processes.

Author : Richard F. Bass
Publisher : Springer Science & Business Media
Page : 408 pages
File Size : 44,6 Mb
Release : 1994-12-16
Category : Mathematics
ISBN : 9780387943879

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Probabilistic Techniques in Analysis by Richard F. Bass Pdf

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 : Rabi Bhattacharya,Edward C. Waymire
Publisher : Springer
Page : 265 pages
File Size : 52,6 Mb
Release : 2017-02-13
Category : Mathematics
ISBN : 9783319479743

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A Basic Course in Probability Theory by Rabi Bhattacharya,Edward C. Waymire Pdf

This text develops the necessary background in probability theory underlying diverse treatments of stochastic processes and their wide-ranging applications. In this second edition, the text has been reorganized for didactic purposes, new exercises have been added and basic theory has been expanded. General Markov dependent sequences and their convergence to equilibrium is the subject of an entirely new chapter. The introduction of conditional expectation and conditional probability very early in the text maintains the pedagogic innovation of the first edition; conditional expectation is illustrated in detail in the context of an expanded treatment of martingales, the Markov property, and the strong Markov property. Weak convergence of probabilities on metric spaces and Brownian motion are two topics to highlight. A selection of large deviation and/or concentration inequalities ranging from those of Chebyshev, Cramer–Chernoff, Bahadur–Rao, to Hoeffding have been added, with illustrative comparisons of their use in practice. This also includes a treatment of the Berry–Esseen error estimate in the central limit theorem. The authors assume mathematical maturity at a graduate level; otherwise the book is suitable for students with varying levels of background in analysis and measure theory. For the reader who needs refreshers, theorems from analysis and measure theory used in the main text are provided in comprehensive appendices, along with their proofs, for ease of reference. Rabi Bhattacharya is Professor of Mathematics at the University of Arizona. Edward Waymire is Professor of Mathematics at Oregon State University. Both authors have co-authored numerous books, including a series of four upcoming graduate textbooks in stochastic processes with applications.

Author : Elton P. Hsu,S. R. S. Varadhan
Publisher : American Mathematical Soc.
Page : 402 pages
File Size : 55,5 Mb
Release : 1999-01-01
Category : Mathematics
ISBN : 0821886886

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Probability Theory and Applications by Elton P. Hsu,S. R. S. Varadhan Pdf

The volume gives a balanced overview of the current status of probability theory. An extensive bibliography for further study and research is included. This unique collection presents several important areas of current research and a valuable survey reflecting the diversity of the field.

Author : Nima Moshayedi
Publisher : World Scientific
Page : 292 pages
File Size : 55,6 Mb
Release : 2022-03-23
Category : Mathematics
ISBN : 9789811243363

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Introduction To Probability Theory: A First Course On The Measure-theoretic Approach by Nima Moshayedi Pdf

This book provides a first introduction to the methods of probability theory by using the modern and rigorous techniques of measure theory and functional analysis. It is geared for undergraduate students, mainly in mathematics and physics majors, but also for students from other subject areas such as economics, finance and engineering. It is an invaluable source, either for a parallel use to a related lecture or for its own purpose of learning it.The first part of the book gives a basic introduction to probability theory. It explains the notions of random events and random variables, probability measures, expectation values, distributions, characteristic functions, independence of random variables, as well as different types of convergence and limit theorems. The first part contains two chapters. The first chapter presents combinatorial aspects of probability theory, and the second chapter delves into the actual introduction to probability theory, which contains the modern probability language. The second part is devoted to some more sophisticated methods such as conditional expectations, martingales and Markov chains. These notions will be fairly accessible after reading the first part. /description --

Author : Daniel Li,Hervé Queffélec
Publisher : Cambridge University Press
Page : 463 pages
File Size : 43,8 Mb
Release : 2017-11-02
Category : Mathematics
ISBN : 9781107160514

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Introduction to Banach Spaces: Analysis and Probability by Daniel Li,Hervé Queffélec Pdf

This first volume of a two-volume overview covers the basic theory of Banach spaces, harmonic analysis and probability.

Author : Bert E. Fristedt,Lawrence F. Gray
Publisher : Springer Science & Business Media
Page : 775 pages
File Size : 45,9 Mb
Release : 2013-11-21
Category : Mathematics
ISBN : 9781489928375

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A Modern Approach to Probability Theory by Bert E. Fristedt,Lawrence F. Gray Pdf

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.

Author : Karl Stromberg
Publisher : Routledge
Page : 330 pages
File Size : 49,8 Mb
Release : 2022-02-27
Category : Mathematics
ISBN : 9781351421614

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Probability For Analysts by Karl Stromberg Pdf

This book will enable researchers and students of analysis to more easily understand research papers in which probabilistic methods are used to prove theorems of analysis, many of which have no other known proofs. The book assumes a course in measure and integration theory but requires little or no background in probability theory. It emplhasizes topics of interest to analysts, including random series, martingales and Brownian motion.

Author : Dugue,E. Lukacs,V. K. Rohatgi
Publisher : Unknown
Page : 200 pages
File Size : 42,9 Mb
Release : 2014-01-15
Category : Electronic
ISBN : 3662135132

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Analytical Methods in Probability Theory by Dugue,E. Lukacs,V. K. Rohatgi Pdf

Author : Albert N. Shiryaev,S. R. S. Varadhan,Ernst L. Presman
Publisher : Springer Science & Business Media
Page : 468 pages
File Size : 51,5 Mb
Release : 2013-01-09
Category : Mathematics
ISBN : 9783642335495

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Prokhorov and Contemporary Probability Theory by Albert N. Shiryaev,S. R. S. Varadhan,Ernst L. Presman Pdf

The role of Yuri Vasilyevich Prokhorov as a prominent mathematician and leading expert in the theory of probability is well known. Even early in his career he obtained substantial results on the validity of the strong law of large numbers and on the estimates (bounds) of the rates of convergence, some of which are the best possible. His findings on limit theorems in metric spaces and particularly functional limit theorems are of exceptional importance. Y.V. Prokhorov developed an original approach to the proof of functional limit theorems, based on the weak convergence of finite dimensional distributions and the condition of tightness of probability measures. The present volume commemorates the 80th birthday of Yuri Vasilyevich Prokhorov. It includes scientific contributions written by his colleagues, friends and pupils, who would like to express their deep respect and sincerest admiration for him and his scientific work.​

Author : Herbert Heyer,Gyula Pap
Publisher : World Scientific
Page : 425 pages
File Size : 54,7 Mb
Release : 2010
Category : Mathematics
ISBN : 9789814282482

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Structural Aspects in the Theory of Probability by Herbert Heyer,Gyula Pap Pdf

The book is conceived as a text accompanying the traditional graduate courses on probability theory. An important feature of this enlarged version is the emphasis on algebraic-topological aspects leading to a wider and deeper understanding of basic theorems such as those on the structure of continuous convolution semigroups and the corresponding processes with independent increments. Fourier transformation ? the method applied within the settings of Banach spaces, locally compact Abelian groups and commutative hypergroups ? is given an in-depth discussion. This powerful analytic tool along with the relevant facts of harmonic analysis make it possible to study certain properties of stochastic processes in dependence of the algebraic-topological structure of their state spaces. In extension of the first edition, the new edition contains chapters on the probability theory of generalized convolution structures such as polynomial and Sturm?Liouville hypergroups, and on the central limit problem for groups such as tori, p-adic groups and solenoids.