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| Author | : Jason Marko Smith |
| Publisher | : |
| Total Pages | : 262 |
| Release | : 2007 |
| Genre | : Gaussian processes |
| ISBN | : |
| Author | : Percy Anthony Pierre |
| Publisher | : |
| Total Pages | : 336 |
| Release | : 1967 |
| Genre | : |
| ISBN | : |
| Author | : Mircea Grigoriu |
| Publisher | : Prentice Hall |
| Total Pages | : 472 |
| Release | : 1995 |
| Genre | : Matlab |
| ISBN | : |
This text defines a variety of non-Gaussian processes, develops methods for generating realizations of non-Gaussian models, and provides methods for finding probabilistic characteristics of the output of linear filters with non-Gaussian inputs.
| Author | : Bruce Hajek |
| Publisher | : Cambridge University Press |
| Total Pages | : 429 |
| Release | : 2015-03-12 |
| Genre | : Technology & Engineering |
| ISBN | : 1316241246 |
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).
| Author | : M. B. Rajarshi |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 121 |
| Release | : 2014-07-08 |
| Genre | : Mathematics |
| ISBN | : 8132207637 |
This work is an overview of statistical inference in stationary, discrete time stochastic processes. Results in the last fifteen years, particularly on non-Gaussian sequences and semi-parametric and non-parametric analysis have been reviewed. The first chapter gives a background of results on martingales and strong mixing sequences, which enable us to generate various classes of CAN estimators in the case of dependent observations. Topics discussed include inference in Markov chains and extension of Markov chains such as Raftery's Mixture Transition Density model and Hidden Markov chains and extensions of ARMA models with a Binomial, Poisson, Geometric, Exponential, Gamma, Weibull, Lognormal, Inverse Gaussian and Cauchy as stationary distributions. It further discusses applications of semi-parametric methods of estimation such as conditional least squares and estimating functions in stochastic models. Construction of confidence intervals based on estimating functions is discussed in some detail. Kernel based estimation of joint density and conditional expectation are also discussed. Bootstrap and other resampling procedures for dependent sequences such as Markov chains, Markov sequences, linear auto-regressive moving average sequences, block based bootstrap for stationary sequences and other block based procedures are also discussed in some detail. This work can be useful for researchers interested in knowing developments in inference in discrete time stochastic processes. It can be used as a material for advanced level research students.
| Author | : Percy A. Pierre |
| Publisher | : |
| Total Pages | : 178 |
| Release | : 1967 |
| Genre | : |
| ISBN | : |
The conclusions of the report are: (1) The expansion coefficients of some common representations of random processes will be independent only when the process is Gaussian; (2) Processes representable on a particular interval in terms of a denumerable sequence of independent random variables will often have sample function properties similar to those of the Gaussian process; (3) The quadratic variation of non-Gaussian processes with sufficiently smooth cumulants is constant for a given interval; (4) The quadratic variation of a non-Gaussian linear process equals the sum of the squares of its jump discontinuities; (5) There is a class of sequences of functionals, say T sub N(x(t)), such that l.i.m. T sub N equals the quadratic variation of the processes in (3). (6) The necessary and sufficient condition for singular detection of a sure signal in Gaussian noise is sufficient for singularity when the noise is any mean square continuous process. (7) Regularity or singularity for signals depending on a random parameter, gamma, is implied by regularity or singularity for signals corresponding to each possible value of gamma when gamma has a discrete distribution or the noise is Gaussian. (8) Singular estimation of certain parameters is sometimes possible under the conditions of singular detections. (9) Some of the spectral conditions which imply singularity for Gaussian random processes continue to imply singularity for non-Gaussian processes with sufficiently smooth cumulants. (10) For other non-Gaussian processes, spectral conditions are irrelevant.
| Author | : Robert M. Gray |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 348 |
| Release | : 2009-07-31 |
| Genre | : Technology & Engineering |
| ISBN | : 1441910905 |
Probability, Random Processes, and Ergodic Properties is for mathematically inclined information/communication theorists and people working in signal processing. It will also interest those working with random or stochastic processes, including mathematicians, statisticians, and economists. Highlights: Complete tour of book and guidelines for use given in Introduction, so readers can see at a glance the topics of interest. Structures mathematics for an engineering audience, with emphasis on engineering applications. New in the Second Edition: Much of the material has been rearranged and revised for pedagogical reasons. The original first chapter has been split in order to allow a more thorough treatment of basic probability before tackling random processes and dynamical systems. The final chapter has been broken into two pieces to provide separate emphasis on process metrics and the ergodic decomposition of affine functionals. Many classic inequalities are now incorporated into the text, along with proofs; and many citations have been added.
| Author | : E. Wong |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 183 |
| Release | : 2013-03-09 |
| Genre | : Mathematics |
| ISBN | : 1475717954 |
| Author | : Venkatarama Krishnan |
| Publisher | : John Wiley & Sons |
| Total Pages | : 739 |
| Release | : 2006-06-27 |
| Genre | : Mathematics |
| ISBN | : 0471998281 |
A resource for probability AND random processes, with hundreds ofworked examples and probability and Fourier transform tables This survival guide in probability and random processes eliminatesthe need to pore through several resources to find a certainformula or table. It offers a compendium of most distributionfunctions used by communication engineers, queuing theoryspecialists, signal processing engineers, biomedical engineers,physicists, and students. Key topics covered include: * Random variables and most of their frequently used discrete andcontinuous probability distribution functions * Moments, transformations, and convergences of randomvariables * Characteristic, generating, and moment-generating functions * Computer generation of random variates * Estimation theory and the associated orthogonalityprinciple * Linear vector spaces and matrix theory with vector and matrixdifferentiation concepts * Vector random variables * Random processes and stationarity concepts * Extensive classification of random processes * Random processes through linear systems and the associated Wienerand Kalman filters * Application of probability in single photon emission tomography(SPECT) More than 400 figures drawn to scale assist readers inunderstanding and applying theory. Many of these figures accompanythe more than 300 examples given to help readers visualize how tosolve the problem at hand. In many instances, worked examples aresolved with more than one approach to illustrate how differentprobability methodologies can work for the same problem. Several probability tables with accuracy up to nine decimal placesare provided in the appendices for quick reference. A specialfeature is the graphical presentation of the commonly occurringFourier transforms, where both time and frequency functions aredrawn to scale. This book is of particular value to undergraduate and graduatestudents in electrical, computer, and civil engineering, as well asstudents in physics and applied mathematics. Engineers, computerscientists, biostatisticians, and researchers in communicationswill also benefit from having a single resource to address mostissues in probability and random processes.
| Author | : John J. Shynk |
| Publisher | : John Wiley & Sons |
| Total Pages | : 850 |
| Release | : 2012-10-15 |
| Genre | : Computers |
| ISBN | : 1118393953 |
Probability, Random Variables, and Random Processes is a comprehensive textbook on probability theory for engineers that provides a more rigorous mathematical framework than is usually encountered in undergraduate courses. It is intended for first-year graduate students who have some familiarity with probability and random variables, though not necessarily of random processes and systems that operate on random signals. It is also appropriate for advanced undergraduate students who have a strong mathematical background. The book has the following features: Several appendices include related material on integration, important inequalities and identities, frequency-domain transforms, and linear algebra. These topics have been included so that the book is relatively self-contained. One appendix contains an extensive summary of 33 random variables and their properties such as moments, characteristic functions, and entropy. Unlike most books on probability, numerous figures have been included to clarify and expand upon important points. Over 600 illustrations and MATLAB plots have been designed to reinforce the material and illustrate the various characterizations and properties of random quantities. Sufficient statistics are covered in detail, as is their connection to parameter estimation techniques. These include classical Bayesian estimation and several optimality criteria: mean-square error, mean-absolute error, maximum likelihood, method of moments, and least squares. The last four chapters provide an introduction to several topics usually studied in subsequent engineering courses: communication systems and information theory; optimal filtering (Wiener and Kalman); adaptive filtering (FIR and IIR); and antenna beamforming, channel equalization, and direction finding. This material is available electronically at the companion website. Probability, Random Variables, and Random Processes is the only textbook on probability for engineers that includes relevant background material, provides extensive summaries of key results, and extends various statistical techniques to a range of applications in signal processing.
