Random Processes By Example
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| Author | : Bruce Hajek |
| Publisher | : Cambridge University Press |
| Total Pages | : 429 |
| Release | : 2015-03-12 |
| Genre | : Technology & Engineering |
| ISBN | : 1316241246 |
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 | : Mikhail Lifshits |
| Publisher | : World Scientific |
| Total Pages | : 232 |
| Release | : 2014-03-07 |
| Genre | : Mathematics |
| ISBN | : 9814522309 |
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.
| Author | : Mikhail Lifshits |
| Publisher | : World Scientific |
| Total Pages | : 232 |
| Release | : 2014 |
| Genre | : Mathematics |
| ISBN | : 9814522295 |
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 OC teletraffic modelOCO. A minor tuning of a few parameters of the model leads to different workload regimes, including Wiener process, fractional Brownian motion and stable L(r)vy 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. Sample Chapter(s). Chapter 1: Preliminaries (367 KB). Contents: Preliminaries: Random Variables: A Summary; From Poisson to Stable Variables; Limit Theorems for Sums and Domains of Attraction; Random Vectors; Random Processes: Random Processes: Main Classes; Examples of Gaussian Random Processes; Random Measures and Stochastic Integrals; Limit Theorems for Poisson Integrals; L(r)vy Processes; Spectral Representations; Convergence of Random Processes; Teletraffic Models: A Model of Service System; Limit Theorems for the Workload; Micropulse Model; Spacial Extensions. Readership: Graduate students and researchers in probability & statist
| Author | : I.A. Ibragimov |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 285 |
| Release | : 2012-12-06 |
| Genre | : Mathematics |
| ISBN | : 1461262755 |
The book deals mainly with three problems involving Gaussian stationary processes. The first problem consists of clarifying the conditions for mutual absolute continuity (equivalence) of probability distributions of a "random process segment" and of finding effective formulas for densities of the equiva lent distributions. Our second problem is to describe the classes of spectral measures corresponding in some sense to regular stationary processes (in par ticular, satisfying the well-known "strong mixing condition") as well as to describe the subclasses associated with "mixing rate". The third problem involves estimation of an unknown mean value of a random process, this random process being stationary except for its mean, i. e. , it is the problem of "distinguishing a signal from stationary noise". Furthermore, we give here auxiliary information (on distributions in Hilbert spaces, properties of sam ple functions, theorems on functions of a complex variable, etc. ). Since 1958 many mathematicians have studied the problem of equivalence of various infinite-dimensional Gaussian distributions (detailed and sys tematic presentation of the basic results can be found, for instance, in [23]). In this book we have considered Gaussian stationary processes and arrived, we believe, at rather definite solutions. The second problem mentioned above is closely related with problems involving ergodic theory of Gaussian dynamic systems as well as prediction theory of stationary processes.
| Author | : Venkatarama Krishnan |
| Publisher | : John Wiley & Sons |
| Total Pages | : 739 |
| Release | : 2006-06-27 |
| Genre | : Mathematics |
| ISBN | : 0471998281 |
A resource for probability AND random processes, with hundreds ofworked examples and probability and Fourier transform tables This survival guide in probability and random processes eliminatesthe need to pore through several resources to find a certainformula or table. It offers a compendium of most distributionfunctions used by communication engineers, queuing theoryspecialists, signal processing engineers, biomedical engineers,physicists, and students. Key topics covered include: * Random variables and most of their frequently used discrete andcontinuous probability distribution functions * Moments, transformations, and convergences of randomvariables * Characteristic, generating, and moment-generating functions * Computer generation of random variates * Estimation theory and the associated orthogonalityprinciple * Linear vector spaces and matrix theory with vector and matrixdifferentiation concepts * Vector random variables * Random processes and stationarity concepts * Extensive classification of random processes * Random processes through linear systems and the associated Wienerand Kalman filters * Application of probability in single photon emission tomography(SPECT) More than 400 figures drawn to scale assist readers inunderstanding and applying theory. Many of these figures accompanythe more than 300 examples given to help readers visualize how tosolve the problem at hand. In many instances, worked examples aresolved with more than one approach to illustrate how differentprobability methodologies can work for the same problem. Several probability tables with accuracy up to nine decimal placesare provided in the appendices for quick reference. A specialfeature is the graphical presentation of the commonly occurringFourier transforms, where both time and frequency functions aredrawn to scale. This book is of particular value to undergraduate and graduatestudents in electrical, computer, and civil engineering, as well asstudents in physics and applied mathematics. Engineers, computerscientists, biostatisticians, and researchers in communicationswill also benefit from having a single resource to address mostissues in probability and random processes.
| Author | : M. Rosenblatt |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 236 |
| Release | : 2012-12-06 |
| Genre | : Mathematics |
| ISBN | : 1461298520 |
This text has as its object an introduction to elements of the theory of random processes. Strictly speaking, only a good background in the topics usually associated with a course in Advanced Calculus (see, for example, the text of Apostol [1]) and the elements of matrix algebra is required although additional background is always helpful. N onethe less a strong effort has been made to keep the required background on the level specified above. This means that a course based on this book would be appropriate for a beginning graduate student or an advanced undergraduate. Previous knowledge of probability theory is not required since the discussion starts with the basic notions of probability theory. Chapters II and III are concerned with discrete probability spaces and elements of the theory of Markov chains respectively. These two chapters thus deal with probability theory for finite or countable models. The object is to present some of the basic ideas and problems of the theory in a discrete context where difficulties of heavy technique and detailed measure theoretic discussions do not obscure the ideas and problems.
| Author | : Howard M. Taylor |
| Publisher | : Academic Press |
| Total Pages | : 410 |
| Release | : 2014-05-10 |
| Genre | : Mathematics |
| ISBN | : 1483269272 |
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 |
| Total Pages | : 320 |
| Release | : 2008-12-22 |
| Genre | : Technology & Engineering |
| ISBN | : 0470322551 |
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 | : Geoffrey Grimmett |
| Publisher | : Oxford University Press |
| Total Pages | : 626 |
| Release | : 2001-05-31 |
| Genre | : Mathematics |
| ISBN | : 9780198572220 |
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 | : Scott Miller |
| Publisher | : Academic Press |
| Total Pages | : 625 |
| Release | : 2012-01-11 |
| Genre | : Mathematics |
| ISBN | : 0123869811 |
Miller and Childers have focused on creating a clear presentation of foundational concepts with specific applications to signal processing and communications, clearly the two areas of most interest to students and instructors in this course. It is aimed at graduate students as well as practicing engineers, and includes unique chapters on narrowband random processes and simulation techniques. The appendices provide a refresher in such areas as linear algebra, set theory, random variables, and more. Probability and Random Processes also includes applications in digital communications, information theory, coding theory, image processing, speech analysis, synthesis and recognition, and other fields. * Exceptional exposition and numerous worked out problems make the book extremely readable and accessible * The authors connect the applications discussed in class to the textbook * The new edition contains more real world signal processing and communications applications * Includes an entire chapter devoted to simulation techniques.
