Probability Theory And Stochastic Processes
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Theory Of Stochastic Objects
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Author : Athanasios Christou Micheas
language : en
Publisher: CRC Press
Release Date : 2018-01-19
Theory Of Stochastic Objects written by Athanasios Christou Micheas and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-01-19 with Mathematics categories.
This book defines and investigates the concept of a random object. To accomplish this task in a natural way, it brings together three major areas; statistical inference, measure-theoretic probability theory and stochastic processes. This point of view has not been explored by existing textbooks; one would need material on real analysis, measure and probability theory, as well as stochastic processes - in addition to at least one text on statistics- to capture the detail and depth of material that has gone into this volume. Presents and illustrates ‘random objects’ in different contexts, under a unified framework, starting with rudimentary results on random variables and random sequences, all the way up to stochastic partial differential equations. Reviews rudimentary probability and introduces statistical inference, from basic to advanced, thus making the transition from basic statistical modeling and estimation to advanced topics more natural and concrete. Compact and comprehensive presentation of the material that will be useful to a reader from the mathematics and statistical sciences, at any stage of their career, either as a graduate student, an instructor, or an academician conducting research and requiring quick references and examples to classic topics. Includes 378 exercises, with the solutions manual available on the book's website. 121 illustrative examples of the concepts presented in the text (many including multiple items in a single example). The book is targeted towards students at the master’s and Ph.D. levels, as well as, academicians in the mathematics, statistics and related disciplines. Basic knowledge of calculus and matrix algebra is required. Prior knowledge of probability or measure theory is welcomed but not necessary.
Probability Theory And Stochastic Processes
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Author : Pierre Brémaud
language : en
Publisher:
Release Date :
Probability Theory And Stochastic Processes written by Pierre Brémaud and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on with Probabilities categories.
Elementary Probability Theory With Stochastic Processes
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Author : K. L. Chung
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-03-09
Elementary Probability Theory With Stochastic Processes written by K. L. Chung and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-03-09 with Mathematics categories.
In the past half-century the theory of probability has grown from a minor isolated theme into a broad and intensive discipline interacting with many other branches of mathematics. At the same time it is playing a centrat role in the mathematization of various applied sciences such as statistics, Opera tions research, biology, economics and psychology-to name a few to which the prefix "mathematical" has so far been firmly attached. The coming-of-age of probability has been reflected in the change of contents of textbooks on the subject. In the old days most of these books showed a visible split personality torn between the combinatorial games of chance and the so-called "theory of errors" centering in the normal distribution. This period ended with the appearance of Feller's dassie treatise (see [Feiler I]t) in 1950, from the manuscript of which I gave my first substantial course in probability. With the passage of time probability theory and its applications have won a place in the college curriculum as a mathematical discipline essential to many fields of study. The elements of the theory are now given at different Ievels, sometimes even before calculus. The present textbook is intended for a course at about the sophomore Ievel. It presupposes no prior acquaintance with the subject and the first three chapters can be read largely without the benefit of calculus.
Introduction To Probability Theory And Stochastic Processes
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Author : John Chiasson
language : en
Publisher: John Wiley & Sons
Release Date : 2013-04-08
Introduction To Probability Theory And Stochastic Processes written by John Chiasson and has been published by John Wiley & Sons this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-04-08 with Mathematics categories.
A unique approach to stochastic processes that connects the mathematical formulation of random processes to their use in applications This book presents an innovative approach to teaching probability theory and stochastic processes based on the binary expansion of the unit interval. Departing from standard pedagogy, it uses the binary expansion of the unit interval to explicitly construct an infinite sequence of independent random variables (of any given distribution) on a single probability space. This construction then provides the framework to understand the mathematical formulation of probability theory for its use in applications. Features include: The theory is presented first for countable sample spaces (Chapters 1-3) and then for uncountable sample spaces (Chapters 4-18) Coverage of the explicit construction of i.i.d. random variables on a single probability space to explain why it is the distribution function rather than the functional form of random variables that matters when it comes to modeling random phenomena Explicit construction of continuous random variables to facilitate the "digestion" of random variables, i.e., how they are used in contrast to how they are defined Explicit construction of continuous random variables to facilitate the two views of expectation: as integration over the underlying probability space (abstract view) or as integration using the density function (usual view) A discussion of the connections between Bernoulli, geometric, and Poisson processes Incorporation of the Johnson-Nyquist noise model and an explanation of why (and when) it is valid to use a delta function to model its autocovariance Comprehensive, astute, and practical, Introduction to Probability Theory and Stochastic Processes is a clear presentation of essential topics for those studying communications, control, machine learning, digital signal processing, computer networks, pattern recognition, image processing, and coding theory.
Combinatorial Methods In The Theory Of Stochastic Processes
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Author : L. Takacs
language : en
Publisher: John Wiley & Sons
Release Date : 1967-01-15
Combinatorial Methods In The Theory Of Stochastic Processes written by L. Takacs and has been published by John Wiley & Sons this book supported file pdf, txt, epub, kindle and other format this book has been release on 1967-01-15 with Mathematics categories.
Introduction To Probability And Stochastic Processes With Applications
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Author : Liliana Blanco Castañeda
language : en
Publisher: John Wiley & Sons
Release Date : 2012-06-26
Introduction To Probability And Stochastic Processes With Applications written by Liliana Blanco Castañeda and has been published by John Wiley & Sons this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-06-26 with Mathematics categories.
An easily accessible, real-world approach to probability and stochastic processes Introduction to Probability and Stochastic Processes with Applications presents a clear, easy-to-understand treatment of probability and stochastic processes, providing readers with a solid foundation they can build upon throughout their careers. With an emphasis on applications in engineering, applied sciences, business and finance, statistics, mathematics, and operations research, the book features numerous real-world examples that illustrate how random phenomena occur in nature and how to use probabilistic techniques to accurately model these phenomena. The authors discuss a broad range of topics, from the basic concepts of probability to advanced topics for further study, including Itô integrals, martingales, and sigma algebras. Additional topical coverage includes: Distributions of discrete and continuous random variables frequently used in applications Random vectors, conditional probability, expectation, and multivariate normal distributions The laws of large numbers, limit theorems, and convergence of sequences of random variables Stochastic processes and related applications, particularly in queueing systems Financial mathematics, including pricing methods such as risk-neutral valuation and the Black-Scholes formula Extensive appendices containing a review of the requisite mathematics and tables of standard distributions for use in applications are provided, and plentiful exercises, problems, and solutions are found throughout. Also, a related website features additional exercises with solutions and supplementary material for classroom use. Introduction to Probability and Stochastic Processes with Applications is an ideal book for probability courses at the upper-undergraduate level. The book is also a valuable reference for researchers and practitioners in the fields of engineering, operations research, and computer science who conduct data analysis to make decisions in their everyday work.
The Theory Of Stochastic Processes
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Author : D.R. Cox
language : en
Publisher: Routledge
Release Date : 2017-09-04
The Theory Of Stochastic Processes written by D.R. Cox and has been published by Routledge this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-09-04 with Mathematics categories.
This book should be of interest to undergraduate and postgraduate students of probability theory.
Probability And Stochastic Processes
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Author : Roy D. Yates
language : en
Publisher: Wiley
Release Date : 1998-08-13
Probability And Stochastic Processes written by Roy D. Yates and has been published by Wiley this book supported file pdf, txt, epub, kindle and other format this book has been release on 1998-08-13 with Technology & Engineering categories.
What Does Winning the Lottery Have To do with Engineering? Whether you're trying to win millions in the lottery or designing a complex computer network, you're applying probability theory. Although you encounter probability applications everywhere, the theory can be deceptively difficult to learn and apply correctly. This text will help you grasp the concepts of probability and stochastic processes and apply them throughout your careers. These concepts are clearly presented throughout the book as a sequence of building blocks that are clearly identified as either an axiom, definition, or theorem. This approach provides you with a better understanding of the material which you'll be able to use to solve practical problems. Key Features: * The text follows a single model that begins with an experiment consisting of a procedure and observations. * The mathematics of discrete random variables appears separately from the mathematics of continuous random variables. * Stochastic processes are introduced in Chapter 6, immediately after the presentation of discrete and continuous random variables. Subsequent material, including central limit theorem approximations, laws of large numbers, and statistical inference, then use examples that reinforce stochastic process concepts. * An abundance of exercises are provided that help students learn how to put the theory to use.
Probability Theory And Stochastic Processes With Applications
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Author : Oliver Knill
language : en
Publisher: Overseas Link Inc
Release Date : 2009
Probability Theory And Stochastic Processes With Applications written by Oliver Knill and has been published by Overseas Link Inc this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009 with Probabilities categories.
Probability Statistics And Stochastic Processes
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Author : Peter Olofsson
language : en
Publisher: John Wiley & Sons
Release Date : 2011-07-20
Probability Statistics And Stochastic Processes written by Peter Olofsson and has been published by John Wiley & Sons this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-07-20 with Mathematics categories.
A mathematical and intuitive approach to probability, statistics, and stochastic processes This textbook provides a unique, balanced approach to probability, statistics, and stochastic processes. Readers gain a solid foundation in all three fields that serves as a stepping stone to more advanced investigations into each area. This text combines a rigorous, calculus-based development of theory with a more intuitive approach that appeals to readers' sense of reason and logic, an approach developed through the author's many years of classroom experience. The text begins with three chapters that develop probability theory and introduce the axioms of probability, random variables, and joint distributions. The next two chapters introduce limit theorems and simulation. Also included is a chapter on statistical inference with a section on Bayesian statistics, which is an important, though often neglected, topic for undergraduate-level texts. Markov chains in discrete and continuous time are also discussed within the book. More than 400 examples are interspersed throughout the text to help illustrate concepts and theory and to assist the reader in developing an intuitive sense of the subject. Readers will find many of the examples to be both entertaining and thought provoking. This is also true for the carefully selected problems that appear at the end of each chapter. This book is an excellent text for upper-level undergraduate courses. While many texts treat probability theory and statistical inference or probability theory and stochastic processes, this text enables students to become proficient in all three of these essential topics. For students in science and engineering who may take only one course in probability theory, mastering all three areas will better prepare them to collect, analyze, and characterize data in their chosen fields.