Stationary Stochastic Processes for Scientists and Engineers

Author: Georg Lindgren,Holger Rootzen,Maria Sandsten
Publisher: CRC Press
ISBN: 1466586192
Category: Mathematics
Page: 330
View: 6256
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.

Stochastic Processes in Science, Engineering and Finance

Author: Frank Beichelt
Publisher: CRC Press
ISBN: 9781420010459
Category: Mathematics
Page: 440
View: 4989
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

Theory and Applications
Author: Georg Lindgren
Publisher: CRC Press
ISBN: 146655780X
Category: Mathematics
Page: 375
View: 4291
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.

Random Differential Equations in Science and Engineering

Author: Soong
Publisher: Academic Press
ISBN: 0080956122
Category: Computers
Page: 326
View: 3376
Random Differential Equations in Science and Engineering

Random Perturbation Methods with Applications in Science and Engineering

Author: Anatoli V. Skorokhod,Frank C. Hoppensteadt,Habib D. Salehi
Publisher: Springer Science & Business Media
ISBN: 0387224467
Category: Mathematics
Page: 490
View: 1374
This book develops methods for describing random dynamical systems, and it illustrats how the methods can be used in a variety of applications. Appeals to researchers and graduate students who require tools to investigate stochastic systems.

Data Analysis and Statistics for Geography, Environmental Science, and Engineering

Author: Miguel F. Acevedo
Publisher: CRC Press
ISBN: 1466592214
Category: Mathematics
Page: 557
View: 4676
Providing a solid foundation for twenty-first-century scientists and engineers, Data Analysis and Statistics for Geography, Environmental Science, and Engineering guides readers in learning quantitative methodology, including how to implement data analysis methods using open-source software. Given the importance of interdisciplinary work in sustainability, the book brings together principles of statistics and probability, multivariate analysis, and spatial analysis methods applicable across a variety of science and engineering disciplines. Learn How to Use a Variety of Data Analysis and Statistics Methods Based on the author’s many years of teaching graduate and undergraduate students, this textbook emphasizes hands-on learning. Organized into two parts, it allows greater flexibility using the material in various countries and types of curricula. The first part covers probability, random variables and inferential statistics, applications of regression, time series analysis, and analysis of spatial point patterns. The second part uses matrix algebra to address multidimensional problems. After a review of matrices, it delves into multiple regression, dependent random processes and autoregressive time series, spatial analysis using geostatistics and spatial regression, discriminant analysis, and a variety of multivariate analyses based on eigenvector methods. Build from Fundamental Concepts to Effective Problem Solving Each chapter starts with conceptual and theoretical material to give a firm foundation in how the methods work. Examples and exercises illustrate the applications and demonstrate how to go from concepts to problem solving. Hands-on computer sessions allow students to grasp the practical implications and learn by doing. Throughout, the computer examples and exercises use seeg and RcmdrPlugin.seeg, open-source R packages developed by the author, which help students acquire the skills to implement and conduct analysis and to analyze the results. This self-contained book offers a unified presentation of data analysis methods for more effective problem solving. With clear, easy-to-follow explanations, the book helps students to develop a solid understanding of basic statistical analysis and prepares them for learning the more advanced and specialized methods they will need in their work.

Stochastic Processes and Their Applications

Author: Frank Beichelt,L. Paul Fatti
Publisher: CRC Press
ISBN: 9780415272322
Category: Mathematics
Page: 338
View: 5988
This book introduces stochastic processes and their applications for students in engineering, industrial statistics, science, operations research, business, and finance. It provides the theoretical foundations for modeling time-dependent random phenomena encountered in these disciplines. Through numerous science and engineering-based examples and exercises, the author presents the subject in a comprehensible, practically oriented way, but he also includes some important proofs and theoretically challenging examples and exercises that will appeal to more mathematically minded readers. Solutions to most of the exercises are included either in an appendix or within the text.

Fundamentals of Linear Systems for Physical Scientists and Engineers

Author: N.N. Puri
Publisher: CRC Press
ISBN: 9781439811580
Category: Technology & Engineering
Page: 899
View: 3695
Thanks to the advent of inexpensive computing, it is possible to analyze, compute, and develop results that were unthinkable in the '60s. Control systems, telecommunications, robotics, speech, vision, and digital signal processing are but a few examples of computing applications. While there are many excellent resources available that focus on one or two topics, few books cover most of the mathematical techniques required for a broader range of applications. Fundamentals of Linear Systems for Physical Scientists and Engineers is such a resource. The book draws from diverse areas of engineering and the physical sciences to cover the fundamentals of linear systems. Assuming no prior knowledge of complex mathematics on the part of the reader, the author uses his nearly 50 years of teaching experience to address all of the necessary mathematical techniques. Original proofs, hundreds of examples, and proven theorems illustrate and clarify the material. An extensive table provides Lyapunov functions for differential equations and conditions of stability for the equilibrium solutions. In an intuitive, step-by-step manner, the book covers a breadth of highly relevant topics in linear systems theory from the introductory level to a more advanced level. The chapter on stochastic processes makes it invaluable for financial engineering applications. Reflecting the pressures in engineering education to provide compact yet comprehensive courses of instruction, this book presents essential linear system theoretic concepts from first principles to relatively advanced, yet general, topics. The book’s self-contained nature and the coverage of both linear continuous- and discrete-time systems set it apart from other texts.

Stochastic Calculus

Applications in Science and Engineering
Author: Mircea Grigoriu
Publisher: Springer Science & Business Media
ISBN: 9780817642426
Category: Mathematics
Page: 774
View: 2038
"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.

System Identification

Advances and Case Studies
Author: Anatoli Torokhti,Raman K. Mehra
Publisher: Elsevier Science & Technology
ISBN: 9780124879508
Category: Estimation theory
Page: 593
View: 3203
In this book, we study theoretical and practical aspects of computing methods for mathematical modelling of nonlinear systems. A number of computing techniques are considered, such as methods of operator approximation with any given accuracy; operator interpolation techniques including a non-Lagrange interpolation; methods of system representation subject to constraints associated with concepts of causality, memory and stationarity; methods of system representation with an accuracy that is the best within a given class of models; methods of covariance matrix estimation; methods for low-rank matrix approximations; hybrid methods based on a combination of iterative procedures and best operator approximation; and methods for information compression and filtering under condition that a filter model should satisfy restrictions associated with causality and different types of memory. As a result, the book represents a blend of new methods in general computational analysis, and specific, but also generic, techniques for study of systems theory ant its particular branches, such as optimal filtering and information compression. - Best operator approximation, - Non-Lagrange interpolation, - Generic Karhunen-Loeve transform - Generalised low-rank matrix approximation - Optimal data compression - Optimal nonlinear filtering

Mathematical Handbook for Scientists and Engineers

Definitions, Theorems, and Formulas for Reference and Review
Author: Granino A. Korn,Theresa M. Korn
Publisher: Courier Corporation
ISBN: 0486320235
Category: Technology & Engineering
Page: 1152
View: 9722
Convenient access to information from every area of mathematics: Fourier transforms, Z transforms, linear and nonlinear programming, calculus of variations, random-process theory, special functions, combinatorial analysis, game theory, much more.

Elementare Wahrscheinlichkeitstheorie und stochastische Prozesse

Author: Kai L. Chung
Publisher: Springer-Verlag
ISBN: 3642670334
Category: Mathematics
Page: 346
View: 5643
Aus den Besprechungen: "Unter den zahlreichen Einführungen in die Wahrscheinlichkeitsrechnung bildet dieses Buch eine erfreuliche Ausnahme. Der Stil einer lebendigen Vorlesung ist über Niederschrift und Übersetzung hinweg erhalten geblieben. In jedes Kapitel wird sehr anschaulich eingeführt. Sinn und Nützlichkeit der mathematischen Formulierungen werden den Lesern nahegebracht. Die wichtigsten Zusammenhänge sind als mathematische Sätze klar formuliert." #FREQUENZ#1

Methods for model selection in applied science and engineering

Author: Richard Van Deventer Field
Publisher: N.A
Page: 476
View: 608

Principles of Neurocomputing for Science and Engineering

Author: Fredric M. Ham,Ivica Kostanic
Publisher: McGraw-Hill Science Engineering
ISBN: 9780070259669
Category: Technology & Engineering
Page: 642
View: 7754
Neurocomputing can be applied to problems such as pattern recognition, optimization, event classification, control and identification of nonlinear systems, and statistical analysis - just to name a few. This book is intended for a course in neural networks."--BOOK JACKET

Stochastic Differential Equations in Science and Engineering

(With CD-ROM)
Author: Douglas Henderson,Peter Plaschko
Publisher: World Scientific
ISBN: 9814480533
Category: Science
Page: 240
View: 1395
' Traditionally, non-quantum physics has been concerned with deterministic equations where the dynamics of the system are completely determined by initial conditions. A century ago the discovery of Brownian motion showed that nature need not be deterministic. However, it is only recently that there has been broad interest in nondeterministic and even chaotic systems, not only in physics but in ecology and economics. On a short term basis, the stock market is nondeterministic and often chaotic. Despite its significance, there are few books available that introduce the reader to modern ideas in stochastic systems. This book provides an introduction to this increasingly important field and includes a number of interesting applications. Contents:Stochastic Variables and Stochastic ProcessesStochastic Differential EquationsThe Fokker–Planck EquationAdvanced TopicsNumerical Solutions of Ordinary Stochastic Differential Equations Readership: Researchers and graduate students in physics, chemistry, and engineering. Keywords:Stochastic Differential Equations;Probability;Chaos;Nonlinear DynamicsKey Features:Each chapter contains a set of exercises to aid understanding of the materialReviews:“The readers will benefit from the illustrations of complex applied phenomena which are well described by using SDEs … At the end of each chapter there are useful exercises with detailed solutions or hints … Anybody working in the area of, or dealing with, stochastic processes, in particular with SDEs, will find interesting topics and/or illustrations.”Zentralblatt MATH '

Maximum-Entropy and Bayesian Methods in Science and Engineering

Volume 2: Applications
Author: G. Erickson,C.R. Smith
Publisher: Springer Science & Business Media
ISBN: 9789027727947
Category: Mathematics
Page: 440
View: 2523
This volume has its origin in the Fifth, Sixth and Seventh Workshops on "Maximum-Entropy and Bayesian Methods in Applied Statistics", held at the University of Wyoming, August 5-8, 1985, and at Seattle University, August 5-8, 1986, and August 4-7, 1987. It was anticipated that the proceedings of these workshops would be combined, so most of the papers were not collected until after the seventh workshop. Because most of the papers in this volume are in the nature of advancing theory or solving specific problems, as opposed to status reports, it is believed that the contents of this volume will be of lasting interest to the Bayesian community. The workshop was organized to bring together researchers from different fields to critically examine maximum-entropy and Bayesian methods in science and engineering as well as other disciplines. Some of the papers were chosen specifically to kindle interest in new areas that may offer new tools or insight to the reader or to stimulate work on pressing problems that appear to be ideally suited to the maximum-entropy or Bayesian method. These workshops and their proceedings could not have been brought to their final form without the support or help of a number of people.

Discrete Stochastic Processes

Author: Robert G. Gallager
Publisher: Springer Science & Business Media
ISBN: 146152329X
Category: Technology & Engineering
Page: 271
View: 3773
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.

Stochastic Processes in Engineering Systems

Author: E. Wong,B. Hajek
Publisher: Springer Science & Business Media
ISBN: 1461250609
Category: Mathematics
Page: 361
View: 436
This book is a revision of Stochastic Processes in Information and Dynamical Systems written by the first author (E.W.) and published in 1971. The book was originally written, and revised, to provide a graduate level text in stochastic processes for students whose primary interest is its applications. It treats both the traditional topic of sta tionary processes in linear time-invariant systems as well as the more modern theory of stochastic systems in which dynamic structure plays a profound role. Our aim is to provide a high-level, yet readily acces sible, treatment of those topics in the theory of continuous-parameter stochastic processes that are important in the analysis of information and dynamical systems. The theory of stochastic processes can easily become abstract. In dealing with it from an applied point of view, we have found it difficult to decide on the appropriate level of rigor. We intend to provide just enough mathematical machinery so that important results can be stated PREFACE vi with precision and clarity; so much ofthe theory of stochastic processes is inherently simple if the suitable framework is provided. The price of providing this framework seems worth paying even though the ul timate goal is in applications and not the mathematics per se.

Stochastic Processes and their Applications

Proceedings of the Symposium Held in Honour of Professor S.K. Srinivasan at the Indian Institute of Technology, Bombay, India, December 27-30, 1990
Author: M.J. Beckmann,M.N. Gopalan,R. Subramanian
Publisher: Springer Science & Business Media
ISBN: 9783540546351
Category: Business & Economics
Page: 292
View: 3366
This volume deals with Stochastic tools with specialreference to applications in the areas of Physics, Biologyand Operations Research. Quitea few of the papers deal withthe applications of the rich theory of point processes inPhysics and Operations Research. A few of the papers dealwith the problems of Inference and Stochastic theory. Inaddition papers of some leading specialists are included.These papers reflect the latest trends in these areas andwill, therefore, be of value and interest to researchers inthese fields.

Stochastic Tools in Mathematics and Science

Author: Alexandre J Chorin,Ole H Hald
Publisher: Springer Science & Business Media
ISBN: 9780387280806
Category: Mathematics
Page: 148
View: 4601
This introduction to probability-based modeling covers basic stochastic tools used in physics, chemistry, engineering and the life sciences. Topics covered include conditional expectations, stochastic processes, Langevin equations, and Markov chain Monte Carlo algorithms. The applications include data assimilation, prediction from partial data, spectral analysis and turbulence. A special feature is the systematic analysis of memory effects.