An Introduction to the Theory of Stationary Random Functions

Author: A. M. Yaglom
Publisher: Courier Corporation
ISBN: 9780486495712
Category : Mathematics
Languages : en
Pages : 258

Book Description
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.

Probability and Random Processes for Electrical and Computer Engineers

Author: John A. Gubner
Publisher: Cambridge University Press
ISBN: 1139457179
Category : Technology & Engineering
Languages : en
Pages : 4

Book Description
The theory of probability is a powerful tool that helps electrical and computer engineers to explain, model, analyze, and design the technology they develop. The text begins at the advanced undergraduate level, assuming only a modest knowledge of probability, and progresses through more complex topics mastered at graduate level. The first five chapters cover the basics of probability and both discrete and continuous random variables. The later chapters have a more specialized coverage, including random vectors, Gaussian random vectors, random processes, Markov Chains, and convergence. Describing tools and results that are used extensively in the field, this is more than a textbook; it is also a reference for researchers working in communications, signal processing, and computer network traffic analysis. With over 300 worked examples, some 800 homework problems, and sections for exam preparation, this is an essential companion for advanced undergraduate and graduate students. Further resources for this title, including solutions (for Instructors only), are available online at www.cambridge.org/9780521864701.

Generalized Linear Models with Random Effects

Author: Youngjo Lee
Publisher: CRC Press
ISBN: 1420011340
Category : Mathematics
Languages : en
Pages : 411

Book Description
Since their introduction in 1972, generalized linear models (GLMs) have proven useful in the generalization of classical normal models. Presenting methods for fitting GLMs with random effects to data, Generalized Linear Models with Random Effects: Unified Analysis via H-likelihood explores a wide range of applications, including combining information over trials (meta-analysis), analysis of frailty models for survival data, genetic epidemiology, and analysis of spatial and temporal models with correlated errors. Written by pioneering authorities in the field, this reference provides an introduction to various theories and examines likelihood inference and GLMs. The authors show how to extend the class of GLMs while retaining as much simplicity as possible. By maximizing and deriving other quantities from h-likelihood, they also demonstrate how to use a single algorithm for all members of the class, resulting in a faster algorithm as compared to existing alternatives. Complementing theory with examples, many of which can be run by using the code supplied on the accompanying CD, this book is beneficial to statisticians and researchers involved in the above applications as well as quality-improvement experiments and missing-data analysis.

Principles of Random Walk

Author: Frank Spitzer
Publisher: Springer Science & Business Media
ISBN: 9780387951546
Category : Mathematics
Languages : en
Pages : 438

Book Description
More than 100 pages of examples and problems illustrate and clarify the presentation."--BOOK JACKET.

Random Functions and Hydrology

Author: Rafael L. Bras
Publisher: Courier Corporation
ISBN: 9780486676265
Category : Technology & Engineering
Languages : en
Pages : 580

Book Description
Advanced-level view of the tools of random processes and field theory as applied to the analysis and synthesis of hydrologic phenomena. Topics include time-series analysis, optimal estimation, optimal interpolation (Kriging), frequency-domain analysis of signals, and linear systems theory. Techniques and examples chosen to illustrate the latest advances in hydrologic signal analysis. Useable as graduate-level text in water resource systems, stochastic hydrology, random processes and signal analysis. 202 illustrations.

Random Walks in the Quarter-Plane

Author: Guy Fayolle
Publisher: Springer Science & Business Media
ISBN: 9783540650478
Category : Mathematics
Languages : en
Pages : 184

Book Description
Promoting original mathematical methods to determine the invariant measure of two-dimensional random walks in domains with boundaries, the authors use Using Riemann surfaces and boundary value problems to propose completely new approaches to solve functional equations of two complex variables. These methods can also be employed to characterize the transient behavior of random walks in the quarter plane.

Evolution of Systems in Random Media

Author: Vladimir S. Korolyuk
Publisher: CRC Press
ISBN: 9780849394058
Category : Mathematics
Languages : en
Pages : 358

Book Description
Evolution of Systems in Random Media is an innovative, application-oriented text that explores stochastic models of evolutionary stochastic systems in random media. Specially designed for researchers and practitioners who do not have a background in random evolutions, the book allows non-experts to explore the potential information and applications that random evolutions can provide.

Random Matrices

Author: Madan Lal Mehta
Publisher: Elsevier
ISBN: 008047411X
Category : Mathematics
Languages : en
Pages : 707

Book Description
Random Matrices gives a coherent and detailed description of analytical methods devised to study random matrices. These methods are critical to the understanding of various fields in in mathematics and mathematical physics, such as nuclear excitations, ultrasonic resonances of structural materials, chaotic systems, the zeros of the Riemann and other zeta functions. More generally they apply to the characteristic energies of any sufficiently complicated system and which have found, since the publication of the second edition, many new applications in active research areas such as quantum gravity, traffic and communications networks or stock movement in the financial markets. This revised and enlarged third edition reflects the latest developements in the field and convey a greater experience with results previously formulated. For example, the theory of skew-orthogoanl and bi-orthogonal polynomials, parallel to that of the widely known and used orthogonal polynomials, is explained here for the first time. - Presentation of many new results in one place for the first time - First time coverage of skew-orthogonal and bi-orthogonal polynomials and their use in the evaluation of some multiple integrals - Fredholm determinants and Painlevé equations - The three Gaussian ensembles (unitary, orthogonal, and symplectic); their n-point correlations, spacing probabilities - Fredholm determinants and inverse scattering theory - Probability densities of random determinants

Ten Lectures on Random Media

Author: Erwin Bolthausen
Publisher: Springer Science & Business Media
ISBN: 9783764367039
Category : Mathematics
Languages : en
Pages : 132

Book Description
The following notes grew out oflectures held during the DMV-Seminar on Random Media in November 1999 at the Mathematics Research Institute of Oberwolfach, and in February-March 2000 at the Ecole Normale Superieure in Paris. In both places the atmosphere was very friendly and stimulating. The positive response of the audience was encouragement enough to write up these notes. I hope they will carryover the enjoyment of the live lectures. I whole heartedly wish to thank Profs. Matthias Kreck and Jean-Franc;ois Le Gall who were respon sible for these two very enjoyable visits, Laurent Miclo for his comments on an earlier version of these notes, and last but not least Erwin Bolthausen who was my accomplice during the DMV-Seminar. A Brief Introduction The main theme of this series of lectures are "Random motions in random me dia". The subject gathers a variety of probabilistic models often originated from physical sciences such as solid state physics, physical chemistry, oceanography, biophysics . . . , in which typically some diffusion mechanism takes place in an inho mogeneous medium. Randomness appears at two levels. It comes in the description of the motion of the particle diffusing in the medium, this is a rather traditional point of view for probability theory; but it also comes in the very description of the medium in which the diffusion takes place.

Solid-State Random Lasers

Author: Mikhail Noginov
Publisher: Springer Science & Business Media
ISBN: 0387239138
Category : Science
Languages : en
Pages : 254

Book Description
Random lasers are the simplest sources of lasers, since they exhibit stimulated emission without a cavity, with the feedback provided by scattering in a gain medium. First proposed in the late 60's, random lasers have grown into a large research field. This book reviews the history and the state of the art of random lasers, providing an outline of the basic models explaining their behavior and describing the recent advances in the field. The major focus is solid-state random lasers, however, random lasers based on liquid dyes with scatterers are also briefly treated. Written with mostly self-contained chapters, Solid-State Random Lasers gives scientists or engineers interested in a particular aspect directly access to the relevant information. Researchers entering the field of random lasers will find in the book an excellent overview, while scientists already working in the field can use the book as a reference source.