An Introduction To The Stationary Random Functions
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Author | : A. M. Yaglom |
Publisher | : Courier Corporation |
Total Pages | : 258 |
Release | : 2004-01-01 |
Genre | : Mathematics |
ISBN | : 9780486495712 |
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.
Author | : Akiva M. Jaglom |
Publisher | : |
Total Pages | : 0 |
Release | : 1965 |
Genre | : Time-series analysis |
ISBN | : |
Author | : Akiva M. Jaglom |
Publisher | : |
Total Pages | : 235 |
Release | : 1962 |
Genre | : |
ISBN | : |
Author | : A.M. Yaglom |
Publisher | : Springer Science & Business Media |
Total Pages | : 267 |
Release | : 2012-12-06 |
Genre | : Mathematics |
ISBN | : 1461246288 |
Correlation Theory of Stationary and Related Random Functions is an elementary introduction to the most important part of the theory dealing only with the first and second moments of these functions. This theory is a significant part of modern probability theory and offers both intrinsic mathematical interest and many concrete and practical applications. Stationary random functions arise in connection with stationary time series which are so important in many areas of engineering and other applications. This book presents the theory in such a way that it can be understood by readers without specialized mathematical backgrounds, requiring only the knowledge of elementary calculus. The first volume in this two-volume exposition contains the main theory; the supplementary notes and references of the second volume consist of detailed discussions of more specialized questions, some more additional material (which assumes a more thorough mathematical background than the rest of the book) and numerous references to the extensive literature.
Author | : A M. Iaglom |
Publisher | : |
Total Pages | : 235 |
Release | : 1962 |
Genre | : Random functions |
ISBN | : |
Author | : A.M. Yaglom |
Publisher | : |
Total Pages | : 0 |
Release | : |
Genre | : |
ISBN | : |
Author | : E. Wong |
Publisher | : Springer Science & Business Media |
Total Pages | : 183 |
Release | : 2013-03-09 |
Genre | : Mathematics |
ISBN | : 1475717954 |
Author | : A. M. Yaglom |
Publisher | : Springer |
Total Pages | : 552 |
Release | : 1987-06-10 |
Genre | : Mathematics |
ISBN | : |
The theory of random functions is a very important and advanced part of modem probability theory, which is very interesting from the mathematical point of view and has many practical applications. In applications, one has to deal particularly often with the special case of stationary random functions. Such functions naturally arise when one considers a series of observations x(t) which depend on the real-valued or integer-valued ar gument t ("time") and do not undergo any systematic changes, but only fluctuate in a disordered manner about some constant mean level. Such a time series x(t) must naturally be described statistically, and in that case the stationary random function is the most appropriate statistical model. Stationary time series constantly occur in nearly all the areas of modem technology (in particular, in electrical and radio engineering, electronics, and automatic control) as well as in all the physical and geophysical sciences, in many other ap mechanics, economics, biology and medicine, and also plied fields. One of the important trends in the recent development of science and engineering is the ever-increasing role of the fluctuation phenomena associated with the stationary disordered time series. Moreover, at present, more general classes of random functions related to a class of stationary random functions have also been appearing quite often in various applied studies and hence have acquired great practical importance.
Author | : Georg Lindgren |
Publisher | : CRC Press |
Total Pages | : 378 |
Release | : 2012-10-01 |
Genre | : Mathematics |
ISBN | : 1466557796 |
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.
Author | : Murray Rosenblatt |
Publisher | : Springer Science & Business Media |
Total Pages | : 253 |
Release | : 2012-12-06 |
Genre | : Mathematics |
ISBN | : 1461251567 |
This book has a dual purpose. One of these is to present material which selec tively will be appropriate for a quarter or semester course in time series analysis and which will cover both the finite parameter and spectral approach. The second object is the presentation of topics of current research interest and some open questions. I mention these now. In particular, there is a discussion in Chapter III of the types of limit theorems that will imply asymptotic nor mality for covariance estimates and smoothings of the periodogram. This dis cussion allows one to get results on the asymptotic distribution of finite para meter estimates that are broader than those usually given in the literature in Chapter IV. A derivation of the asymptotic distribution for spectral (second order) estimates is given under an assumption of strong mixing in Chapter V. A discussion of higher order cumulant spectra and their large sample properties under appropriate moment conditions follows in Chapter VI. Probability density, conditional probability density and regression estimates are considered in Chapter VII under conditions of short range dependence. Chapter VIII deals with a number of topics. At first estimates for the structure function of a large class of non-Gaussian linear processes are constructed. One can determine much more about this structure or transfer function in the non-Gaussian case than one can for Gaussian processes. In particular, one can determine almost all the phase information.