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Author: Gregory K. Miller
Publisher: Wiley-Interscience
ISBN:
Category : Mathematics
Languages : en
Pages : 496
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Book Description
Improve Your Probability of Mastering This Topic This book takes an innovative approach to calculus-based probability theory, considering it within a framework for creating models of random phenomena. The author focuses on the synthesis of stochastic models concurrent with the development of distribution theory while also introducing the reader to basic statistical inference. In this way, the major stochastic processes are blended with coverage of probability laws, random variables, and distribution theory, equipping the reader to be a true problem solver and critical thinker. Deliberately conversational in tone, Probability is written for students in junior- or senior-level probability courses majoring in mathematics, statistics, computer science, or engineering. The book offers a lucid and mathematicallysound introduction to how probability is used to model random behavior in the natural world. The text contains the following chapters: Modeling Sets and Functions Probability Laws I: Building on the Axioms Probability Laws II: Results of Conditioning Random Variables and Stochastic Processes Discrete Random Variables and Applications in Stochastic Processes Continuous Random Variables and Applications in Stochastic Processes Covariance and Correlation Among Random Variables Included exercises cover a wealth of additional concepts, such as conditional independence, Simpson's paradox, acceptance sampling, geometric probability, simulation, exponential families of distributions, Jensen's inequality, and many non-standard probability distributions.
Author: Gregory K. Miller
Publisher: Wiley-Interscience
ISBN:
Category : Mathematics
Languages : en
Pages : 496
Get Book Here
Book Description
Improve Your Probability of Mastering This Topic This book takes an innovative approach to calculus-based probability theory, considering it within a framework for creating models of random phenomena. The author focuses on the synthesis of stochastic models concurrent with the development of distribution theory while also introducing the reader to basic statistical inference. In this way, the major stochastic processes are blended with coverage of probability laws, random variables, and distribution theory, equipping the reader to be a true problem solver and critical thinker. Deliberately conversational in tone, Probability is written for students in junior- or senior-level probability courses majoring in mathematics, statistics, computer science, or engineering. The book offers a lucid and mathematicallysound introduction to how probability is used to model random behavior in the natural world. The text contains the following chapters: Modeling Sets and Functions Probability Laws I: Building on the Axioms Probability Laws II: Results of Conditioning Random Variables and Stochastic Processes Discrete Random Variables and Applications in Stochastic Processes Continuous Random Variables and Applications in Stochastic Processes Covariance and Correlation Among Random Variables Included exercises cover a wealth of additional concepts, such as conditional independence, Simpson's paradox, acceptance sampling, geometric probability, simulation, exponential families of distributions, Jensen's inequality, and many non-standard probability distributions.
Author: Bruce Hajek
Publisher: Cambridge University Press
ISBN: 1316241246
Category : Technology & Engineering
Languages : en
Pages : 429
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Book Description
This engaging introduction to random processes provides students with the critical tools needed to design and evaluate engineering systems that must operate reliably in uncertain environments. A brief review of probability theory and real analysis of deterministic functions sets the stage for understanding random processes, whilst the underlying measure theoretic notions are explained in an intuitive, straightforward style. Students will learn to manage the complexity of randomness through the use of simple classes of random processes, statistical means and correlations, asymptotic analysis, sampling, and effective algorithms. Key topics covered include: • Calculus of random processes in linear systems • Kalman and Wiener filtering • Hidden Markov models for statistical inference • The estimation maximization (EM) algorithm • An introduction to martingales and concentration inequalities. Understanding of the key concepts is reinforced through over 100 worked examples and 300 thoroughly tested homework problems (half of which are solved in detail at the end of the book).
Author: Igor N. Kovalenko
Publisher: CRC Press
ISBN: 9780849328701
Category : Mathematics
Languages : en
Pages : 456
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Book Description
Devising and investigating random processes that describe mathematical models of phenomena is a major aspect of probability theory applications. Stochastic methods have penetrated into an unimaginably wide scope of problems encountered by researchers who need stochastic methods to solve problems and further their studies. This handbook supplies the knowledge you need on the modern theory of random processes. Packed with methods, Models of Random Processes: A Handbook for Mathematicians and Engineers presents definitions and properties on such widespread processes as Poisson, Markov, semi-Markov, Gaussian, and branching processes, and on special processes such as cluster, self-exiting, double stochastic Poisson, Gauss-Poisson, and extremal processes occurring in a variety of different practical problems. The handbook is based on an axiomatic definition of probability space, with strict definitions and constructions of random processes. Emphasis is placed on the constructive definition of each class of random processes, so that a process is explicitly defined by a sequence of independent random variables and can easily be implemented into the modelling. Models of Random Processes: A Handbook for Mathematicians and Engineers will be useful to researchers, engineers, postgraduate students and teachers in the fields of mathematics, physics, engineering, operations research, system analysis, econometrics, and many others.
Author: Howard M. Taylor
Publisher: Academic Press
ISBN: 1483269272
Category : Mathematics
Languages : en
Pages : 410
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Book Description
An Introduction to Stochastic Modeling provides information pertinent to the standard concepts and methods of stochastic modeling. This book presents the rich diversity of applications of stochastic processes in the sciences. Organized into nine chapters, this book begins with an overview of diverse types of stochastic models, which predicts a set of possible outcomes weighed by their likelihoods or probabilities. This text then provides exercises in the applications of simple stochastic analysis to appropriate problems. Other chapters consider the study of general functions of independent, identically distributed, nonnegative random variables representing the successive intervals between renewals. This book discusses as well the numerous examples of Markov branching processes that arise naturally in various scientific disciplines. The final chapter deals with queueing models, which aid the design process by predicting system performance. This book is a valuable resource for students of engineering and management science. Engineers will also find this book useful.
Author: James J. Solberg
Publisher: John Wiley & Sons
ISBN: 0470322551
Category : Technology & Engineering
Languages : en
Pages : 320
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Book Description
Modeling Random Processes for Engineers and Managers provides students with a "gentle" introduction to stochastic processes, emphasizing full explanations and many examples rather than formal mathematical theorems and proofs. The text offers an accessible entry into a very useful and versatile set of tools for dealing with uncertainty and variation. Many practical examples of models, as well as complete explanations of the thought process required to create them, motivate the presentation of the computational methods. In addition, the text contains a previously unpublished computational approach to solving many of the equations that occur in Markov processes. Modeling Random Processes is intended to serve as an introduction, but more advanced students can use the case studies and problems to expand their understanding of practical uses of the theory.
Author: Oliver Ibe
Publisher: Academic Press
ISBN: 0128010355
Category : Mathematics
Languages : en
Pages : 457
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Book Description
The long-awaited revision of Fundamentals of Applied Probability and Random Processes expands on the central components that made the first edition a classic. The title is based on the premise that engineers use probability as a modeling tool, and that probability can be applied to the solution of engineering problems. Engineers and students studying probability and random processes also need to analyze data, and thus need some knowledge of statistics. This book is designed to provide students with a thorough grounding in probability and stochastic processes, demonstrate their applicability to real-world problems, and introduce the basics of statistics. The book's clear writing style and homework problems make it ideal for the classroom or for self-study. - Demonstrates concepts with more than 100 illustrations, including 2 dozen new drawings - Expands readers' understanding of disruptive statistics in a new chapter (chapter 8) - Provides new chapter on Introduction to Random Processes with 14 new illustrations and tables explaining key concepts. - Includes two chapters devoted to the two branches of statistics, namely descriptive statistics (chapter 8) and inferential (or inductive) statistics (chapter 9).
Author: Gennady Samoradnitsky
Publisher: Routledge
ISBN: 1351414801
Category : Mathematics
Languages : en
Pages : 632
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Book Description
This book serves as a standard reference, making this area accessible not only to researchers in probability and statistics, but also to graduate students and practitioners. The book assumes only a first-year graduate course in probability. Each chapter begins with a brief overview and concludes with a wide range of exercises at varying levels of difficulty. The authors supply detailed hints for the more challenging problems, and cover many advances made in recent years.
Author: Oliver Ibe
Publisher: Newnes
ISBN: 0124078397
Category : Mathematics
Languages : en
Pages : 515
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Book Description
Markov processes are processes that have limited memory. In particular, their dependence on the past is only through the previous state. They are used to model the behavior of many systems including communications systems, transportation networks, image segmentation and analysis, biological systems and DNA sequence analysis, random atomic motion and diffusion in physics, social mobility, population studies, epidemiology, animal and insect migration, queueing systems, resource management, dams, financial engineering, actuarial science, and decision systems. Covering a wide range of areas of application of Markov processes, this second edition is revised to highlight the most important aspects as well as the most recent trends and applications of Markov processes. The author spent over 16 years in the industry before returning to academia, and he has applied many of the principles covered in this book in multiple research projects. Therefore, this is an applications-oriented book that also includes enough theory to provide a solid ground in the subject for the reader. - Presents both the theory and applications of the different aspects of Markov processes - Includes numerous solved examples as well as detailed diagrams that make it easier to understand the principle being presented - Discusses different applications of hidden Markov models, such as DNA sequence analysis and speech analysis.
Author: Geoffrey Grimmett
Publisher: Oxford University Press
ISBN: 9780198572220
Category : Mathematics
Languages : en
Pages : 626
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Book Description
This textbook provides a wide-ranging and entertaining indroduction to probability and random processes and many of their practical applications. It includes many exercises and problems with solutions.
Author: Mikhail Lifshits
Publisher: World Scientific
ISBN: 9814522309
Category : Mathematics
Languages : en
Pages : 232
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Book Description
This volume first introduces the mathematical tools necessary for understanding and working with a broad class of applied stochastic models. The toolbox includes Gaussian processes, independently scattered measures such as Gaussian white noise and Poisson random measures, stochastic integrals, compound Poisson, infinitely divisible and stable distributions and processes.Next, it illustrates general concepts by handling a transparent but rich example of a “teletraffic model”. A minor tuning of a few parameters of the model leads to different workload regimes, including Wiener process, fractional Brownian motion and stable Lévy process. The simplicity of the dependence mechanism used in the model enables us to get a clear understanding of long and short range dependence phenomena. The model also shows how light or heavy distribution tails lead to continuous Gaussian processes or to processes with jumps in the limiting regime. Finally, in this volume, readers will find discussions on the multivariate extensions that admit a variety of completely different applied interpretations.The reader will quickly become familiar with key concepts that form a language for many major probabilistic models of real world phenomena but are often neglected in more traditional courses of stochastic processes.
