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Six classic papers, selected to meet the needs of physicists, applied mathematicians, and engineers, include contributions by S. Chandrasekhar, G. E. Uhlenbeck, L. S. Ornstein, Ming Chen Wang, others. 1954 edition.
In two main sections, this volume covers peaks of random functions and the effects of noise on relays and nonlinear self-excited oscillations in the presence of noise. Includes bibliographic references and index.
Stochastic processes are an essential part of numerous branches of physics, as well as in biology, chemistry, and finance. This textbook provides a solid understanding of stochastic processes and stochastic calculus in physics, without the need for measure theory. In avoiding measure theory, this textbook gives readers the tools necessary to use stochastic methods in research with a minimum of mathematical background. Coverage of the more exotic Levy processes is included, as is a concise account of numerical methods for simulating stochastic systems driven by Gaussian noise. The book concludes with a non-technical introduction to the concepts and jargon of measure-theoretic probability theory. With over 70 exercises, this textbook is an easily accessible introduction to stochastic processes and their applications, as well as methods for numerical simulation, for graduate students and researchers in physics.
What is radar? What systems are currently in use? How do they work? Understanding Radar Systems provides engineers and scientists with answers to these critical questions, focusing on actual radar systems in use today. It's the perfect resource for those just entering the field or a quick refresher for experienced practitioners. The book leads readers through the specialized language and calculations that comprise the complex world of modern radar engineering as seen in dozens of state-of-the-art radar systems. The authors stress practical concepts that apply to all radar, keeping math to a minimum. Most of the book is based on real radar systems rather than theoretical studies. The result is a valuable, easy-to-use guide that makes the difficult parts of the field easier and helps readers do performance calculations quickly and easily.
In 1945, very early in the history of the development of a rigorous analytical theory of probability, Feller (1945) wrote a paper called “The fundamental limit theorems in probability” in which he set out what he considered to be “the two most important limit theorems in the modern theory of probability: the central limit theorem and the recently discovered ... ‘Kolmogoroff’s cel ebrated law of the iterated logarithm’ ”. A little later in the article he added to these, via a charming description, the “little brother (of the central limit theo rem), the weak law of large numbers”, and also the strong law of large num bers, which he considers as a close relative of the law of the iterated logarithm. Feller might well have added to these also the beautiful and highly applicable results of renewal theory, which at the time he himself together with eminent colleagues were vigorously producing. Feller’s introductory remarks include the visionary: “The history of probability shows that our problems must be treated in their greatest generality: only in this way can we hope to discover the most natural tools and to open channels for new progress. This remark leads naturally to that characteristic of our theory which makes it attractive beyond its importance for various applications: a combination of an amazing generality with algebraic precision.
Featuring an extensive 40 page tutorial introduction, this carefully compiled anthology of 65 of the most important papers on phase-locked loops and clock recovery circuits brings you comprehensive coverage of the field-all in one self-contained volume. You'll gain an understanding of the analysis, design, simulation, and implementation of phase-locked loops and clock recovery circuits in CMOS and bipolar technologies along with valuable insights into the issues and trade-offs associated with phase locked systems for high speed, low power, and low noise.
This book presents various results and techniques from the theory of stochastic processes that are useful in the study of stochastic problems in the natural sciences. The main focus is analytical methods, although numerical methods and statistical inference methodologies for studying diffusion processes are also presented. The goal is the development of techniques that are applicable to a wide variety of stochastic models that appear in physics, chemistry and other natural sciences. Applications such as stochastic resonance, Brownian motion in periodic potentials and Brownian motors are studied and the connection between diffusion processes and time-dependent statistical mechanics is elucidated. The book contains a large number of illustrations, examples, and exercises. It will be useful for graduate-level courses on stochastic processes for students in applied mathematics, physics and engineering. Many of the topics covered in this book (reversible diffusions, convergence to equilibrium for diffusion processes, inference methods for stochastic differential equations, derivation of the generalized Langevin equation, exit time problems) cannot be easily found in textbook form and will be useful to both researchers and students interested in the applications of stochastic processes.
Aims At The Level Between That Of Elementary Probability Texts And Advanced Works On Stochastic Processes. The Pre-Requisites Are A Course On Elementary Probability Theory And Statistics, And A Course On Advanced Calculus. The Theoretical Results Developed Have Been Followed By A Large Number Of Illustrative Examples. These Have Been Supplemented By Numerous Exercises, Answers To Most Of Which Are Also Given. It Will Suit As A Text For Advanced Undergraduate, Postgraduate And Research Level Course In Applied Mathematics, Statistics, Operations Research, Computer Science, Different Branches Of Engineering, Telecommunications, Business And Management, Economics, Life Sciences And So On. A Review Of The Book In American Mathematical Monthly (December 82) Gives This Book Special Positive Emphasis As A Textbook As Follows: 'Of The Dozen Or More Texts Published In The Last Five Years Aimed At The Students With A Background Of A First Course In Probability And Statistics But Not Yet To Measure Theory, This Is The Clear Choice. An Extremely Well Organized, Lucidly Written Text With Numerous Problems, Examples And Reference T* (With T* Where T Denotes Textbook And * Denotes Special Positive Emphasis). The Current Enlarged And Revised Edition, While Retaining The Structure And Adhering To The Objective As Well As Philosophy Of The Earlier Edition, Removes The Deficiencies, Updates The Material And The References And Aims At A Border Perspective With Substantial Additions And Wider Coverage.
This book contains contributions from various authors on different important topics related with probabilistic methods used for the design of structures. Initially several of the papers were prepared for advanced courses on structural reliability or on probabilistic methods for structural design. These courses have been held in different countries and have been given by different groups of lecturers. They were aimed at engineers and researchers who already had some exposure to structural reliability methods and thus they presented overviews of the work in the various topics. The book includes a selection of those contributions, which can be of support for future courses or for engineers and researchers that want to have an update on specific topics. It is considered a complement to the existing textbooks on structural reliability, which normally ensure the coverage of the basic topics but then are not extensive enough to cover some more specialised aspects. In addition to the contributions drawn from those lectures there are several papers that have been prepared specifically for this book, aiming at complementing the others in providing an overall account of the recent advances in the field. It is with sadness that in the meanwhile we have seen the disappearance of two of the contributors to the book and, in fact two of the early contributors to this field.
This two-part treatment covers the general theory of stationary random functions and the Wiener-Kolmogorov theory of extrapolation and interpolation of random sequences and processes. Beginning with the simplest concepts, it covers the correlation function, the ergodic theorem, homogenous random fields, and general rational spectral densities, among other topics. Numerous examples appear throughout the text, with emphasis on the physical meaning of mathematical concepts. Although rigorous in its treatment, this is essentially an introduction, and the sole prerequisites are a rudimentary knowledge of probability and complex variable theory. 1962 edition.