Books in Probability theory and stochastic processes

Probability and Random Processes

1st Edition
January 3, 1992
Scott Miller + 1 more
English
Hardback
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eBook
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Probability and Random Processes provides a clear presentation of foundational concepts with specific applications to signal processing and communications, clearly the two areas of most interest to students and instructors in this course. It includes unique chapters on narrowband random processes and simulation techniques. It also includes applications in digital communications, information theory, coding theory, image processing, speech analysis, synthesis and recognition, and other fields. The appendices provide a refresher in such areas as linear algebra, set theory, random variables, and more. Exceptional exposition and numerous worked out problems make the book extremely readable and accessible. It is meant for practicing engineers as well as graduate students.

Truth, Possibility and Probability

1st Edition
Volume 166
June 20, 1991
R. Chuaqui
English
eBook
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Anyone involved in the philosophy of science is naturally drawn into the study of the foundations of probability. Different interpretations of probability, based on competing philosophical ideas, lead to different statistical techniques, and frequently to mutually contradictory consequences.This unique book presents a new interpretation of probability, rooted in the traditional interpretation that was current in the 17th and 18th centuries. Mathematical models are constructed based on this interpretation, and statistical inference and decision theory are applied, including some examples in artificial intelligence, solving the main foundational problems. Nonstandard analysis is extensively developed for the construction of the models and in some of the proofs. Many nonstandard theorems are proved, some of them new, in particular, a representation theorem that asserts that any stochastic process can be approximated by a process defined over a space with equiprobable outcomes.

Stochastic Analysis

1st Edition
May 10, 2014
Eddy Mayer-Wolf + 2 more
English
eBook
9 7 8 1 4 8 3 2 1 8 7 0 0

Stochastic Analysis: Liber Amicorum for Moshe Zakai focuses on stochastic differential equations, nonlinear filtering, two-parameter martingales, Wiener space analysis, and related topics. The selection first ponders on conformally invariant and reflection positive random fields in two dimensions; real time architectures for the Zakai equation and applications; and quadratic approximation by linear systems controlled from partial observations. Discussions focus on predicted miss, review of basic sequential detection problems, multigrid algorithms for the Zakai equation, invariant test functions and regularity, and reflection positivity. The text then takes a look at a model of stochastic differential equation in Hubert spaces applicable to Navier Stokes equation in dimension 2; wavelets as attractors of random dynamical systems; and Markov properties for certain random fields. The publication examines the anatomy of a low-noise jump filter, nonlinear filtering with small observation noise, and closed form characteristic functions for certain random variables related to Brownian motion. Topics include derivation of characteristic functions for the examples, proof of the theorem, sequential quadratic variation test, asymptotic optimal filters, mean decision time, and asymptotic optimal filters. The selection is a valuable reference for researchers interested in stochastic analysis.

Order Statistics & Inference

1st Edition
June 28, 2014
Narayanaswamy Balakrishnan + 1 more
English
eBook
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The literature on order statistics and inferenc eis quite extensive and covers a large number of fields ,but most of it is dispersed throughout numerous publications. This volume is the consolidtion of the most important results and places an emphasis on estimation. Both theoretical and computational procedures are presented to meet the needs of researchers, professionals, and students. The methods of estimation discussed are well-illustrated with numerous practical examples from both the physical and life sciences, including sociology,psychology... nd electrical and chemical engineering. A complete, comprehensive bibliography is included so the book can be used both aas a text and reference.

Sample Size Methodology

1st Edition
December 2, 2012
M. M. Desu
English
eBook
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One of the most important problems in designing an experiment or a survey is sample size determination and this book presents the currently available methodology. It includes both random sampling from standard probability distributions and from finite populations. Also discussed is sample size determination for estimating parameters in a Bayesian setting by considering the posterior distribution of the parameter and specifying the necessary requirements. The determination of the sample size is considered for ranking and selection problems as well as for the design of clinical trials. Appropriate techniques for attacking the general question of sample size determination in problems of estimation, tests of hypotheses, selection, and clinical trial design are all presented, and will help the reader in formulating an appropriate problem of sample size and in obtaining the solution. The book can be used as a text in a senior-level or a graduate course on sample size methodology.

Probability, Statistics, and Queueing Theory

2nd Edition
August 28, 1990
Arnold O. Allen
English
eBook
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This is a textbook on applied probability and statistics with computer science applications for students at the upper undergraduate level. It may also be used as a self study book for the practicing computer science professional. The successful first edition of this book proved extremely useful to students who need to use probability, statistics and queueing theory to solve problems in other fields, such as engineering, physics, operations research, and management science. The book has also been successfully used for courses in queueing theory for operations research students. This second edition includes a new chapter on regression as well as more than twice as many exercises at the end of each chapter. While the emphasis is the same as in the first edition, this new book makes more extensive use of available personal computer software, such as Minitab and Mathematica.

Stochastic Wave Propagation

1st Edition
December 2, 2012
K. Sobczyk
English
eBook
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This is a concise, unified exposition of the existing methods of analysis of linear stochastic waves with particular reference to the most recent results. Both scalar and vector waves are considered. Principal attention is concentrated on wave propagation in stochastic media and wave scattering at stochastic surfaces. However, discussion extends also to various mathematical aspects of stochastic wave equations and problems of modelling stochastic media.

Markov Chains

1st Edition
Volume 11
May 1, 1984
D. Revuz
English
Hardback
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eBook
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This is the revised and augmented edition of a now classic book which is an introduction to sub-Markovian kernels on general measurable spaces and their associated homogeneous Markov chains. The first part, an expository text on the foundations of the subject, is intended for post-graduate students. A study of potential theory, the basic classification of chains according to their asymptotic behaviour and the celebrated Chacon-Ornstein theorem are examined in detail.The second part of the book is at a more advanced level and includes a treatment of random walks on general locally compact abelian groups. Further chapters develop renewal theory, an introduction to Martin boundary and the study of chains recurrent in the Harris sense. Finally, the last chapter deals with the construction of chains starting from a kernel satisfying some kind of maximum principle.

Probability Theory with Applications

1st Edition
February 1, 1984
M. M. Rao
English
eBook
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The material in this book is designed for a standard graduate course on probability theory, including some important applications. It was prepared from the sets of lecture notes for a course that I have taught several times over the past 20 years. The present version reflects the reactions of my audiences as well as some of the textbooks that I used.

Stochastic Modelling of Social Processes

1st Edition
May 10, 2014
Andreas Diekmann + 1 more
English
eBook
9 7 8 1 4 8 3 2 6 6 5 6 5

Stochastic Modelling of Social Processes provides information pertinent to the development in the field of stochastic modeling and its applications in the social sciences. This book demonstrates that stochastic models can fulfill the goals of explanation and prediction. Organized into nine chapters, this book begins with an overview of stochastic models that fulfill normative, predictive, and structural–analytic roles with the aid of the theory of probability. This text then examines the study of labor market structures using analysis of job and career mobility, which is one of the approaches taken by sociologists in research on the labor market. Other chapters consider the characteristic trends and patterns from data on divorces. This book discusses as well the two approaches of stochastic modeling of social processes, namely competing risk models and semi-Markov processes. The final chapter deals with the practical application of regression models of survival data. This book is a valuable resource for social scientists and statisticians.

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