Introduction To Probability Theory And Stochastic Processes

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Introduction to Probability Theory and Stochastic Processes

John Chiasson
Introduction to Probability Theory and Stochastic Processes Book PDF

Author : John Chiasson
Publisher : John Wiley & Sons
Page : 0 pages
File Size : 44,8 Mb
Release : 2013-04-08
Category : Mathematics
ISBN : 9781118382790

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Introduction to Probability Theory and Stochastic Processes by John Chiasson Pdf

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.

Introduction to Probability and Stochastic Processes with Applications

Liliana Blanco Castañeda,Viswanathan Arunachalam,Selvamuthu Dharmaraja
Introduction to Probability and Stochastic Processes with Applications Book PDF

Author : Liliana Blanco Castañeda,Viswanathan Arunachalam,Selvamuthu Dharmaraja
Publisher : John Wiley & Sons
Page : 741 pages
File Size : 45,7 Mb
Release : 2014-08-21
Category : Mathematics
ISBN : 9781118344965

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Introduction to Probability and Stochastic Processes with Applications by Liliana Blanco Castañeda,Viswanathan Arunachalam,Selvamuthu Dharmaraja Pdf

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.

Elementary Probability Theory

Kai Lai Chung,Farid AitSahlia
Elementary Probability Theory Book PDF

Author : Kai Lai Chung,Farid AitSahlia
Publisher : Springer Science & Business Media
Page : 411 pages
File Size : 40,7 Mb
Release : 2012-11-12
Category : Mathematics
ISBN : 9780387215488

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Elementary Probability Theory by Kai Lai Chung,Farid AitSahlia Pdf

This book provides an introduction to probability theory and its applications. The emphasis is on essential probabilistic reasoning, which is illustrated with a large number of samples. The fourth edition adds material related to mathematical finance as well as expansions on stable laws and martingales. From the reviews: "Almost thirty years after its first edition, this charming book continues to be an excellent text for teaching and for self study." -- STATISTICAL PAPERS

An Introduction to Probability and Stochastic Processes

Marc A. Berger
An Introduction to Probability and Stochastic Processes Book PDF

Author : Marc A. Berger
Publisher : Springer Science & Business Media
Page : 228 pages
File Size : 47,8 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9781461227267

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An Introduction to Probability and Stochastic Processes by Marc A. Berger Pdf

These notes were written as a result of my having taught a "nonmeasure theoretic" course in probability and stochastic processes a few times at the Weizmann Institute in Israel. I have tried to follow two principles. The first is to prove things "probabilistically" whenever possible without recourse to other branches of mathematics and in a notation that is as "probabilistic" as possible. Thus, for example, the asymptotics of pn for large n, where P is a stochastic matrix, is developed in Section V by using passage probabilities and hitting times rather than, say, pulling in Perron Frobenius theory or spectral analysis. Similarly in Section II the joint normal distribution is studied through conditional expectation rather than quadratic forms. The second principle I have tried to follow is to only prove results in their simple forms and to try to eliminate any minor technical com putations from proofs, so as to expose the most important steps. Steps in proofs or derivations that involve algebra or basic calculus are not shown; only steps involving, say, the use of independence or a dominated convergence argument or an assumptjon in a theorem are displayed. For example, in proving inversion formulas for characteristic functions I omit steps involving evaluation of basic trigonometric integrals and display details only where use is made of Fubini's Theorem or the Dominated Convergence Theorem.

An Introduction to Probability and Stochastic Processes

James L. Melsa,Andrew P. Sage
An Introduction to Probability and Stochastic Processes Book PDF

Author : James L. Melsa,Andrew P. Sage
Publisher : Courier Corporation
Page : 420 pages
File Size : 51,9 Mb
Release : 2013-01-01
Category : Mathematics
ISBN : 9780486490991

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An Introduction to Probability and Stochastic Processes by James L. Melsa,Andrew P. Sage Pdf

Detailed coverage of probability theory, random variables and their functions, stochastic processes, linear system response to stochastic processes, Gaussian and Markov processes, and stochastic differential equations. 1973 edition.

Elementary Probability Theory with Stochastic Processes

K. L. Chung
Elementary Probability Theory with Stochastic Processes Book PDF

Author : K. L. Chung
Publisher : Springer Science & Business Media
Page : 332 pages
File Size : 45,6 Mb
Release : 2013-03-09
Category : Mathematics
ISBN : 9781475739732

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Elementary Probability Theory with Stochastic Processes by K. L. Chung Pdf

This book provides an elementary introduction to probability theory and its applications. The emphasis is on essential probabilistic reasoning, amply motivated, explained and illustrated with a large number of carefully selected samples. The fourth edition adds material related to mathematical finance, as well as expansions on stable laws and martingales.

Introduction to Probability Theory and Stochastic Processes

John Chiasson
Introduction to Probability Theory and Stochastic Processes Book PDF

Author : John Chiasson
Publisher : Wiley
Page : 984 pages
File Size : 49,9 Mb
Release : 2013-03-29
Category : Mathematics
ISBN : 1118615107

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Introduction to Probability Theory and Stochastic Processes by John Chiasson Pdf

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.

Probability Theory and Stochastic Processes

Pierre Brémaud
Probability Theory and Stochastic Processes Book PDF

Author : Pierre Brémaud
Publisher : Springer Nature
Page : 713 pages
File Size : 41,8 Mb
Release : 2020-04-07
Category : Mathematics
ISBN : 9783030401832

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Probability Theory and Stochastic Processes by Pierre Brémaud Pdf

The ultimate objective of this book is to present a panoramic view of the main stochastic processes which have an impact on applications, with complete proofs and exercises. Random processes play a central role in the applied sciences, including operations research, insurance, finance, biology, physics, computer and communications networks, and signal processing. In order to help the reader to reach a level of technical autonomy sufficient to understand the presented models, this book includes a reasonable dose of probability theory. On the other hand, the study of stochastic processes gives an opportunity to apply the main theoretical results of probability theory beyond classroom examples and in a non-trivial manner that makes this discipline look more attractive to the applications-oriented student. One can distinguish three parts of this book. The first four chapters are about probability theory, Chapters 5 to 8 concern random sequences, or discrete-time stochastic processes, and the rest of the book focuses on stochastic processes and point processes. There is sufficient modularity for the instructor or the self-teaching reader to design a course or a study program adapted to her/his specific needs. This book is in a large measure self-contained.

Introduction to Probability, Statistics, and Random Processes

Hossein Pishro-Nik
Introduction to Probability Statistics and Random Processes Book PDF

Author : Hossein Pishro-Nik
Publisher : Unknown
Page : 746 pages
File Size : 40,7 Mb
Release : 2014-08-15
Category : Probabilities
ISBN : 0990637204

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Introduction to Probability, Statistics, and Random Processes by Hossein Pishro-Nik Pdf

The book covers basic concepts such as random experiments, probability axioms, conditional probability, and counting methods, single and multiple random variables (discrete, continuous, and mixed), as well as moment-generating functions, characteristic functions, random vectors, and inequalities; limit theorems and convergence; introduction to Bayesian and classical statistics; random processes including processing of random signals, Poisson processes, discrete-time and continuous-time Markov chains, and Brownian motion; simulation using MATLAB and R.

A First Look At Stochastic Processes

Jeffrey S Rosenthal
A First Look At Stochastic Processes Book PDF

Author : Jeffrey S Rosenthal
Publisher : World Scientific
Page : 213 pages
File Size : 52,9 Mb
Release : 2019-09-26
Category : Mathematics
ISBN : 9789811207921

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A First Look At Stochastic Processes by Jeffrey S Rosenthal Pdf

This textbook introduces the theory of stochastic processes, that is, randomness which proceeds in time. Using concrete examples like repeated gambling and jumping frogs, it presents fundamental mathematical results through simple, clear, logical theorems and examples. It covers in detail such essential material as Markov chain recurrence criteria, the Markov chain convergence theorem, and optional stopping theorems for martingales. The final chapter provides a brief introduction to Brownian motion, Markov processes in continuous time and space, Poisson processes, and renewal theory.Interspersed throughout are applications to such topics as gambler's ruin probabilities, random walks on graphs, sequence waiting times, branching processes, stock option pricing, and Markov Chain Monte Carlo (MCMC) algorithms.The focus is always on making the theory as well-motivated and accessible as possible, to allow students and readers to learn this fascinating subject as easily and painlessly as possible.

Introduction To Stochastic Processes

Mu-fa Chen,Yong-hua Mao
Introduction To Stochastic Processes Book PDF

Author : Mu-fa Chen,Yong-hua Mao
Publisher : World Scientific
Page : 245 pages
File Size : 52,6 Mb
Release : 2021-05-25
Category : Mathematics
ISBN : 9789814740326

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Introduction To Stochastic Processes by Mu-fa Chen,Yong-hua Mao Pdf

The objective of this book is to introduce the elements of stochastic processes in a rather concise manner where we present the two most important parts — Markov chains and stochastic analysis. The readers are led directly to the core of the main topics to be treated in the context. Further details and additional materials are left to a section containing abundant exercises for further reading and studying.In the part on Markov chains, the focus is on the ergodicity. By using the minimal nonnegative solution method, we deal with the recurrence and various types of ergodicity. This is done step by step, from finite state spaces to denumerable state spaces, and from discrete time to continuous time. The methods of proofs adopt modern techniques, such as coupling and duality methods. Some very new results are included, such as the estimate of the spectral gap. The structure and proofs in the first part are rather different from other existing textbooks on Markov chains.In the part on stochastic analysis, we cover the martingale theory and Brownian motions, the stochastic integral and stochastic differential equations with emphasis on one dimension, and the multidimensional stochastic integral and stochastic equation based on semimartingales. We introduce three important topics here: the Feynman-Kac formula, random time transform and Girsanov transform. As an essential application of the probability theory in classical mathematics, we also deal with the famous Brunn-Minkowski inequality in convex geometry.This book also features modern probability theory that is used in different fields, such as MCMC, or even deterministic areas: convex geometry and number theory. It provides a new and direct routine for students going through the classical Markov chains to the modern stochastic analysis.

Probability and Stochastic Processes

Roy D. Yates,David J. Goodman
Probability and Stochastic Processes Book PDF

Author : Roy D. Yates,David J. Goodman
Publisher : John Wiley & Sons
Page : 514 pages
File Size : 54,7 Mb
Release : 2014-01-28
Category : Mathematics
ISBN : 9781118324561

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Probability and Stochastic Processes by Roy D. Yates,David J. Goodman Pdf

This text introduces engineering students to probability theory and stochastic processes. Along with thorough mathematical development of the subject, the book presents intuitive explanations of key points in order to give students the insights they need to apply math to practical engineering problems. The first seven chapters contain the core material that is essential to any introductory course. In one-semester undergraduate courses, instructors can select material from the remaining chapters to meet their individual goals. Graduate courses can cover all chapters in one semester.

Introduction to Stochastic Processes with R

Robert P. Dobrow
Introduction to Stochastic Processes with R Book PDF

Author : Robert P. Dobrow
Publisher : John Wiley & Sons
Page : 503 pages
File Size : 52,6 Mb
Release : 2016-03-07
Category : Mathematics
ISBN : 9781118740651

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Introduction to Stochastic Processes with R by Robert P. Dobrow Pdf

An introduction to stochastic processes through the use of R Introduction to Stochastic Processes with R is an accessible and well-balanced presentation of the theory of stochastic processes, with an emphasis on real-world applications of probability theory in the natural and social sciences. The use of simulation, by means of the popular statistical software R, makes theoretical results come alive with practical, hands-on demonstrations. Written by a highly-qualified expert in the field, the author presents numerous examples from a wide array of disciplines, which are used to illustrate concepts and highlight computational and theoretical results. Developing readers’ problem-solving skills and mathematical maturity, Introduction to Stochastic Processes with R features: More than 200 examples and 600 end-of-chapter exercises A tutorial for getting started with R, and appendices that contain review material in probability and matrix algebra Discussions of many timely and stimulating topics including Markov chain Monte Carlo, random walk on graphs, card shuffling, Black–Scholes options pricing, applications in biology and genetics, cryptography, martingales, and stochastic calculus Introductions to mathematics as needed in order to suit readers at many mathematical levels A companion web site that includes relevant data files as well as all R code and scripts used throughout the book Introduction to Stochastic Processes with R is an ideal textbook for an introductory course in stochastic processes. The book is aimed at undergraduate and beginning graduate-level students in the science, technology, engineering, and mathematics disciplines. The book is also an excellent reference for applied mathematicians and statisticians who are interested in a review of the topic.

Introduction to Probability Models

Sheldon M. Ross
Introduction to Probability Models Book PDF

Author : Sheldon M. Ross
Publisher : Academic Press
Page : 801 pages
File Size : 45,5 Mb
Release : 2006-12-11
Category : Mathematics
ISBN : 9780123756879

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Introduction to Probability Models by Sheldon M. Ross Pdf

Introduction to Probability Models, Tenth Edition, provides an introduction to elementary probability theory and stochastic processes. There are two approaches to the study of probability theory. One is heuristic and nonrigorous, and attempts to develop in students an intuitive feel for the subject that enables him or her to think probabilistically. The other approach attempts a rigorous development of probability by using the tools of measure theory. The first approach is employed in this text. The book begins by introducing basic concepts of probability theory, such as the random variable, conditional probability, and conditional expectation. This is followed by discussions of stochastic processes, including Markov chains and Poison processes. The remaining chapters cover queuing, reliability theory, Brownian motion, and simulation. Many examples are worked out throughout the text, along with exercises to be solved by students. This book will be particularly useful to those interested in learning how probability theory can be applied to the study of phenomena in fields such as engineering, computer science, management science, the physical and social sciences, and operations research. Ideally, this text would be used in a one-year course in probability models, or a one-semester course in introductory probability theory or a course in elementary stochastic processes. New to this Edition: 65% new chapter material including coverage of finite capacity queues, insurance risk models and Markov chains Contains compulsory material for new Exam 3 of the Society of Actuaries containing several sections in the new exams Updated data, and a list of commonly used notations and equations, a robust ancillary package, including a ISM, SSM, and test bank Includes SPSS PASW Modeler and SAS JMP software packages which are widely used in the field Hallmark features: Superior writing style Excellent exercises and examples covering the wide breadth of coverage of probability topics Real-world applications in engineering, science, business and economics

Theory of Probability and Random Processes

Leonid Koralov,Yakov G. Sinai
Theory of Probability and Random Processes Book PDF

Author : Leonid Koralov,Yakov G. Sinai
Publisher : Springer Science & Business Media
Page : 346 pages
File Size : 44,7 Mb
Release : 2007-08-10
Category : Mathematics
ISBN : 9783540688297

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Theory of Probability and Random Processes by Leonid Koralov,Yakov G. Sinai Pdf

A one-year course in probability theory and the theory of random processes, taught at Princeton University to undergraduate and graduate students, forms the core of this book. It provides a comprehensive and self-contained exposition of classical probability theory and the theory of random processes. The book includes detailed discussion of Lebesgue integration, Markov chains, random walks, laws of large numbers, limit theorems, and their relation to Renormalization Group theory. It also includes the theory of stationary random processes, martingales, generalized random processes, and Brownian motion.