## Stationary Stochastic Processes for Scientists and Engineers

**Author**: Georg Lindgren,Holger Rootzen,Maria Sandsten

**Publisher:**CRC Press

**ISBN:**1466586192

**Category:**Mathematics

**Page:**330

**View:**2210

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Stochastic processes are indispensable tools for development and research in signal and image processing, automatic control, oceanography, structural reliability, environmetrics, climatology, econometrics, and many other areas of science and engineering. Suitable for a one-semester course, Stationary Stochastic Processes for Scientists and Engineers teaches students how to use these processes efficiently. Carefully balancing mathematical rigor and ease of exposition, the book provides students with a sufficient understanding of the theory and a practical appreciation of how it is used in real-life situations. Special emphasis is on the interpretation of various statistical models and concepts as well as the types of questions statistical analysis can answer. The text first introduces numerous examples from signal processing, economics, and general natural sciences and technology. It then covers the estimation of mean value and covariance functions, properties of stationary Poisson processes, Fourier analysis of the covariance function (spectral analysis), and the Gaussian distribution. The book also focuses on input-output relations in linear filters, describes discrete-time auto-regressive and moving average processes, and explains how to solve linear stochastic differential equations. It concludes with frequency analysis and estimation of spectral densities. With a focus on model building and interpreting the statistical concepts, this classroom-tested book conveys a broad understanding of the mechanisms that generate stationary stochastic processes. By combining theory and applications, the text gives students a well-rounded introduction to these processes. To enable hands-on practice, MATLAB® code is available online.

## Stationary Stochastic Processes

*Theory and Applications*

**Author**: Georg Lindgren

**Publisher:**CRC Press

**ISBN:**1466557796

**Category:**Mathematics

**Page:**375

**View:**6393

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Intended for a second course in stationary processes, Stationary Stochastic Processes: Theory and Applications presents the theory behind the field’s widely scattered applications in engineering and science. In addition, it reviews sample function properties and spectral representations for stationary processes and fields, including a portion on stationary point processes. Features Presents and illustrates the fundamental correlation and spectral methods for stochastic processes and random fields Explains how the basic theory is used in special applications like detection theory and signal processing, spatial statistics, and reliability Motivates mathematical theory from a statistical model-building viewpoint Introduces a selection of special topics, including extreme value theory, filter theory, long-range dependence, and point processes Provides more than 100 exercises with hints to solutions and selected full solutions This book covers key topics such as ergodicity, crossing problems, and extremes, and opens the doors to a selection of special topics, like extreme value theory, filter theory, long-range dependence, and point processes, and includes many exercises and examples to illustrate the theory. Precise in mathematical details without being pedantic, Stationary Stochastic Processes: Theory and Applications is for the student with some experience with stochastic processes and a desire for deeper understanding without getting bogged down in abstract mathematics.

## Stochastic Processes in Science, Engineering and Finance

**Author**: Frank Beichelt

**Publisher:**CRC Press

**ISBN:**9781420010459

**Category:**Mathematics

**Page:**440

**View:**3911

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This book presents a self-contained introduction to stochastic processes with emphasis on their applications in science, engineering, finance, computer science, and operations research. It provides theoretical foundations for modeling time-dependent random phenomena in these areas and illustrates their application by analyzing numerous practical examples. The treatment assumes few prerequisites, requiring only the standard mathematical maturity acquired by undergraduate applied science students. It includes an introductory chapter that summarizes the basic probability theory needed as background. Numerous exercises reinforce the concepts and techniques discussed and allow readers to assess their grasp of the subject. Solutions to most of the exercises are provided in an appendix. While focused primarily on practical aspects, the presentation includes some important proofs along with more challenging examples and exercises for those more theoretically inclined. Mastering the contents of this book prepares readers to apply stochastic modeling in their own fields and enables them to work more creatively with software designed for dealing with the data analysis aspects of stochastic processes.

## Stationary Stochastic Processes. (MN-8)

**Author**: Takeyuki Hida

**Publisher:**Princeton University Press

**ISBN:**1400868572

**Category:**Mathematics

**Page:**174

**View:**4850

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Encompassing both introductory and more advanced research material, these notes deal with the author's contributions to stochastic processes and focus on Brownian motion processes and its derivative white noise. Originally published in 1970. The Princeton Legacy Library uses the latest print-on-demand technology to again make available previously out-of-print books from the distinguished backlist of Princeton University Press. These editions preserve the original texts of these important books while presenting them in durable paperback and hardcover editions. The goal of the Princeton Legacy Library is to vastly increase access to the rich scholarly heritage found in the thousands of books published by Princeton University Press since its founding in 1905.

## Probability and Stochastic Processes for Engineers

**Author**: Carl W. Helstrom

**Publisher:**Macmillan Coll Division

**ISBN:**N.A

**Category:**Mathematics

**Page:**610

**View:**5279

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## Stochastic Processes

*Theory for Applications*

**Author**: Robert G. Gallager

**Publisher:**Cambridge University Press

**ISBN:**1107435315

**Category:**Technology & Engineering

**Page:**568

**View:**3188

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This definitive textbook provides a solid introduction to discrete and continuous stochastic processes, tackling a complex field in a way that instils a deep understanding of the relevant mathematical principles, and develops an intuitive grasp of the way these principles can be applied to modelling real-world systems. It includes a careful review of elementary probability and detailed coverage of Poisson, Gaussian and Markov processes with richly varied queuing applications. The theory and applications of inference, hypothesis testing, estimation, random walks, large deviations, martingales and investments are developed. Written by one of the world's leading information theorists, evolving over twenty years of graduate classroom teaching and enriched by over 300 exercises, this is an exceptional resource for anyone looking to develop their understanding of stochastic processes.

## Stochastic Processes, Finance and Control

*A Festschrift in Honor of Robert J. Elliott*

**Author**: Robert J. Elliot

**Publisher:**World Scientific

**ISBN:**9814383309

**Category:**Mathematics

**Page:**588

**View:**5387

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This Festschrift is dedicated to Robert J Elliott on the occasion of his 70th birthday It brings together a collection of chapters by distinguished and eminent scholars in the fields of stochastic processes, filtering and control, as well as their applications to mathematical finance It presents cutting edge developments in these fields and is a valuable source of references for researchers, graduate students and market practitioners in mathematical finance and financial engineering Topics include the theory of stochastic processes, differential and stochastic games, mathematical finance, filtering and control.

## Stochastic Processes

*An Introduction, Third Edition*

**Author**: Peter Watts Jones,Peter Smith

**Publisher:**CRC Press

**ISBN:**1498778127

**Category:**Mathematics

**Page:**255

**View:**8451

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Based on a well-established and popular course taught by the authors over many years, Stochastic Processes: An Introduction, Third Edition, discusses the modelling and analysis of random experiments, where processes evolve over time. The text begins with a review of relevant fundamental probability. It then covers gambling problems, random walks, and Markov chains. The authors go on to discuss random processes continuous in time, including Poisson, birth and death processes, and general population models, and present an extended discussion on the analysis of associated stationary processes in queues. The book also explores reliability and other random processes, such as branching, martingales, and simple epidemics. A new chapter describing Brownian motion, where the outcomes are continuously observed over continuous time, is included. Further applications, worked examples and problems, and biographical details have been added to this edition. Much of the text has been reworked. The appendix contains key results in probability for reference. This concise, updated book makes the material accessible, highlighting simple applications and examples. A solutions manual with fully worked answers of all end-of-chapter problems, and Mathematica® and R programs illustrating many processes discussed in the book, can be downloaded from crcpress.com.

## Introduction to Stochastic Processes

**Author**: Erhan Cinlar

**Publisher:**Courier Corporation

**ISBN:**0486276325

**Category:**Mathematics

**Page:**416

**View:**9188

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Clear presentation employs methods that recognize computer-related aspects of theory. Topics include expectations and independence, Bernoulli processes and sums of independent random variables, Markov chains, renewal theory, more. 1975 edition.

## Applied Probability and Stochastic Processes

**Author**: Frank Beichelt

**Publisher:**CRC Press

**ISBN:**1482257653

**Category:**Business & Economics

**Page:**562

**View:**5610

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Applied Probability and Stochastic Processes, Second Edition presents a self-contained introduction to elementary probability theory and stochastic processes with a special emphasis on their applications in science, engineering, finance, computer science, and operations research. It covers the theoretical foundations for modeling time-dependent random phenomena in these areas and illustrates applications through the analysis of numerous practical examples. The author draws on his 50 years of experience in the field to give your students a better understanding of probability theory and stochastic processes and enable them to use stochastic modeling in their work. New to the Second Edition Completely rewritten part on probability theory—now more than double in size New sections on time series analysis, random walks, branching processes, and spectral analysis of stationary stochastic processes Comprehensive numerical discussions of examples, which replace the more theoretically challenging sections Additional examples, exercises, and figures Presenting the material in a student-friendly, application-oriented manner, this non-measure theoretic text only assumes a mathematical maturity that applied science students acquire during their undergraduate studies in mathematics. Many exercises allow students to assess their understanding of the topics. In addition, the book occasionally describes connections between probabilistic concepts and corresponding statistical approaches to facilitate comprehension. Some important proofs and challenging examples and exercises are also included for more theoretically interested readers.

## Selected Papers on Noise and Stochastic Processes

**Author**: Nelson Wax

**Publisher:**Courier Corporation

**ISBN:**0486798267

**Category:**Technology & Engineering

**Page:**352

**View:**7122

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These six classic papers on stochastic process were selected to meet the needs of professionals and advanced undergraduates and graduate students in physics, applied mathematics, and engineering. Contents include: "Stochastic Problems in Physics and Astronomy" by S. Chandrasekhar from Reviews of Modern Physics, Vol. 15, No. 1 "On the Theory of Brownian Motion" by G. E. Uhlenbeck and L. S. Ornstein from Physical Review, Vol. 36, No. 3 "On the Theory of the Brownian Motion II" by Ming Chen Wang and G. E. Uhlenbeck from Reviews of Modern Physics, Vol. 17, Nos. 2 and 3 "Mathematical Analysis of Random Noise" by S. O. Rice from Bell System Technical Journal, Vols. 23 and 24 "Random Walk and the Theory of Brownian Motion" by Mark Kac from American Mathematical Monthly, Vol. 54, No. 7 "The Brownian Movement and Stochastic Equations" by J. L. Doob from Annals of Mathematics, Vol. 43, No. 2

## Random Processes for Engineers

**Author**: Bruce Hajek

**Publisher:**Cambridge University Press

**ISBN:**1316241246

**Category:**Technology & Engineering

**Page:**N.A

**View:**2372

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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).

## Stochastic Modeling

*Analysis and Simulation*

**Author**: Barry L. Nelson

**Publisher:**Courier Corporation

**ISBN:**0486139948

**Category:**Mathematics

**Page:**336

**View:**3055

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Coherent introduction to techniques also offers a guide to the mathematical, numerical, and simulation tools of systems analysis. Includes formulation of models, analysis, and interpretation of results. 1995 edition.

## Adventures in Stochastic Processes

**Author**: Sidney I. Resnick

**Publisher:**Springer Science & Business Media

**ISBN:**1461203872

**Category:**Mathematics

**Page:**626

**View:**8253

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Stochastic processes are necessary ingredients for building models of a wide variety of phenomena exhibiting time varying randomness. This text offers easy access to this fundamental topic for many students of applied sciences at many levels. It includes examples, exercises, applications, and computational procedures. It is uniquely useful for beginners and non-beginners in the field. No knowledge of measure theory is presumed.

## Stochastic Calculus

*Applications in Science and Engineering*

**Author**: Mircea Grigoriu

**Publisher:**Springer Science & Business Media

**ISBN:**9780817642426

**Category:**Mathematics

**Page:**774

**View:**1147

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"This self-contained text may be used for several graduate courses and as an important reference resource for applied scientists interested in analytical and numerical methods for solving stochastic problems."--BOOK JACKET.

## Discrete Stochastic Processes

**Author**: Robert G. Gallager

**Publisher:**Springer Science & Business Media

**ISBN:**146152329X

**Category:**Technology & Engineering

**Page:**271

**View:**3187

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Stochastic processes are found in probabilistic systems that evolve with time. Discrete stochastic processes change by only integer time steps (for some time scale), or are characterized by discrete occurrences at arbitrary times. Discrete Stochastic Processes helps the reader develop the understanding and intuition necessary to apply stochastic process theory in engineering, science and operations research. The book approaches the subject via many simple examples which build insight into the structure of stochastic processes and the general effect of these phenomena in real systems. The book presents mathematical ideas without recourse to measure theory, using only minimal mathematical analysis. In the proofs and explanations, clarity is favored over formal rigor, and simplicity over generality. Numerous examples are given to show how results fail to hold when all the conditions are not satisfied. Audience: An excellent textbook for a graduate level course in engineering and operations research. Also an invaluable reference for all those requiring a deeper understanding of the subject.

## Stationary and Related Stochastic Processes

*Sample Function Properties and Their Applications*

**Author**: Harald Cramér,M. Ross Leadbetter

**Publisher:**Courier Corporation

**ISBN:**0486153355

**Category:**Mathematics

**Page:**368

**View:**2144

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This graduate-level text offers a comprehensive account of the general theory of stationary processes and develops the foundations of the general theory of stochastic processes, examines processes with a continuous-time parameter, more. 1967 edition.

## Multidimensional Second Order Stochastic Processes

**Author**: Yûichirô Kakihara

**Publisher:**World Scientific

**ISBN:**9814497894

**Category:**Mathematics

**Page:**344

**View:**2944

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This book provides a research-expository treatment of infinite-dimensional nonstationary stochastic processes or time series. Stochastic measures and scalar or operator bimeasures are fully discussed to develop integral representations of various classes of nonstationary processes such as harmonizable, V-bounded, Cramér and Karhunen classes and also the stationary class. Emphasis is on the use of functional, harmonic analysis as well as probability theory. Applications are made from the probabilistic and statistical points of view to prediction problems, Kalman filter, sampling theorems and strong laws of large numbers. Readers may find that the covariance kernel analysis is emphasized and it reveals another aspect of stochastic processes. This book is intended not only for probabilists and statisticians, but also for communication engineers. Contents:Introduction and PreliminariesHilbert Modules and Covariance KernelsStochastic Measures and Operator-Valued BimeasuresMultidimensional Stochastic ProcessesSpecial TopicsApplications Readership: Mathematicians, statisticians, communication engineers and physicists. keywords:Multidimensional Process;Stationary Process;Harmonizable Process;V-Bounded Process;Cramer Class;Karhunen Class;Stochastic Measure;Operator Bimeasure;Hilbert Module;Sampling Theorem;Operator Covariance “This book is particularly useful for both specialists and researchers starting to work in the field of multidimensional analysis and multidimensional random processes.” Mathematical Reviews

## Topics in Stochastic Processes

*Probability and Mathematical Statistics: A Series of Monographs and Textbooks*

**Author**: Robert B. Ash,Melvin F. Gardner

**Publisher:**Academic Press

**ISBN:**1483191435

**Category:**Mathematics

**Page:**332

**View:**6929

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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.

## Classical and Spatial Stochastic Processes

*With Applications to Biology*

**Author**: Rinaldo B. Schinazi

**Publisher:**Springer

**ISBN:**1493918699

**Category:**Mathematics

**Page:**268

**View:**6121

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The revised and expanded edition of this textbook presents the concepts and applications of random processes with the same illuminating simplicity as its first edition, but with the notable addition of substantial modern material on biological modeling. While still treating many important problems in fields such as engineering and mathematical physics, the book also focuses on the highly relevant topics of cancerous mutations, influenza evolution, drug resistance, and immune response. The models used elegantly apply various classical stochastic models presented earlier in the text, and exercises are included throughout to reinforce essential concepts. The second edition of Classical and Spatial Stochastic Processes is suitable as a textbook for courses in stochastic processes at the advanced-undergraduate and graduate levels, or as a self-study resource for researchers and practitioners in mathematics, engineering, physics, and mathematical biology. Reviews of the first edition: An appetizing textbook for a first course in stochastic processes. It guides the reader in a very clever manner from classical ideas to some of the most interesting modern results. ... All essential facts are presented with clear proofs, illustrated by beautiful examples. ... The book is well organized, has informative chapter summaries, and presents interesting exercises. The clear proofs are concentrated at the ends of the chapters making it easy to find the results. The style is a good balance of mathematical rigorosity and user-friendly explanation. —Biometric Journal This small book is well-written and well-organized. ... Only simple results are treated ... but at the same time many ideas needed for more complicated cases are hidden and in fact very close. The second part is a really elementary introduction to the area of spatial processes. ... All sections are easily readable and it is rather tentative for the reviewer to learn them more deeply by organizing a course based on this book. The reader can be really surprised seeing how simple the lectures on these complicated topics can be. At the same time such important questions as phase transitions and their properties for some models and the estimates for certain critical values are discussed rigorously. ... This is indeed a first course on stochastic processes and also a masterful introduction to some modern chapters of the theory. —Zentralblatt Math