Robert B. Ash – författare
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9 produkter
9 produkter
Inbunden, Engelska, 1999
1 128 kr
Skickas inom 10-15 vardagar
Probability and Measure Theory, Second Edition, is a text for a graduate-level course in probability that includes essential background topics in analysis. It provides extensive coverage of conditional probability and expectation, strong laws of large numbers, martingale theory, the central limit theorem, ergodic theory, and Brownian motion. Clear, readable style Solutions to many problems presented in text Solutions manual for instructors Material new to the second edition on ergodic theory, Brownian motion, and convergence theorems used in statistics No knowledge of general topology required, just basic analysis and metric spaces Efficient organization
Häftad, Engelska, 2008
280 kr
Skickas inom 3-6 vardagar
Häftad, Engelska, 2010
175 kr
Skickas inom 3-6 vardagar
Inbunden, Engelska, 2011
193 kr
Skickas inom 3-6 vardagar
Häftad, Engelska, 1993
1 471 kr
Skickas inom 5-8 vardagar
This book fills an educational void by adapting unique classroom-tested techniques that students find most congenial...that strip the shroud of mystery from an esoteric subject...that prepare students for applications of calculus in later courses.
E-bok
PDF, Engelska, 2014783 kr
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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.
E-bok
PDF, Engelska, 2014783 kr
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Topics in Stochastic Processes covers specific processes that have a definite physical interpretation and that explicit numerical results can be obtained. This book contains five chapters and begins with the L2 stochastic processes and the concept of prediction theory. The next chapter discusses the principles of ergodic theorem to real analysis, Markov chains, and information theory. Another chapter deals with the sample function behavior of continuous parameter processes. This chapter also explores the general properties of Martingales and Markov processes, as well as the one-dimensional Brownian motion. The aim of this chapter is to illustrate those concepts and constructions that are basic in any discussion of continuous parameter processes, and to provide insights to more advanced material on Markov processes and potential theory. The final chapter demonstrates the use of theory of continuous parameter processes to develop the Itô stochastic integral. This chapter also provides the solution of stochastic differential equations. This book will be of great value to mathematicians, engineers, and physicists.
E-bok
PDF, Engelska, 2014783 kr
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Complex Variables deals with complex variables and covers topics ranging from Cauchy''s theorem to entire functions, families of analytic functions, and the prime number theorem. Major applications of the basic principles, such as residue theory, the Poisson integral, and analytic continuation are given. Comprised of seven chapters, this book begins with an introduction to the basic definitions and concepts in complex variables such as the extended plane, analytic and elementary functions, and Cauchy-Riemann equations. The first chapter defines the integral of a complex function on a path in the complex plane and develops the machinery to prove an elementary version of Cauchy''s theorem. Some applications, including the basic properties of power series, are then presented. Subsequent chapters focus on the general Cauchy theorem and its applications; entire functions; families of analytic functions; and the prime number theorem. The geometric intuition underlying the concept of winding number is emphasized. The linear space viewpoint is also discussed, along with analytic number theory, residue theory, and the Poisson integral. This book is intended primarily for students who are just beginning their professional training in mathematics.
E-bok
PDF, Engelska, 2014783 kr
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Measure, Integration, and Functional Analysis deals with the mathematical concepts of measure, integration, and functional analysis. The fundamentals of measure and integration theory are discussed, along with the interplay between measure theory and topology. Comprised of four chapters, this book begins with an overview of the basic concepts of the theory of measure and integration as a prelude to the study of probability, harmonic analysis, linear space theory, and other areas of mathematics. The reader is then introduced to a variety of applications of the basic integration theory developed in the previous chapter, with particular reference to the Radon-Nikodym theorem. The third chapter is devoted to functional analysis, with emphasis on various structures that can be defined on vector spaces. The final chapter considers the connection between measure theory and topology and looks at a result that is a companion to the monotone class theorem, together with the Daniell integral and measures on topological spaces. The book concludes with an assessment of measures on uncountably infinite product spaces and the weak convergence of measures. This book is intended for mathematics majors, most likely seniors or beginning graduate students, and students of engineering and physics who use measure theory or functional analysis in their work.