Markov processes are among the most important stochastic processes for both theory and applications. This book develops the general theory of these processes and applies this theory to various special examples. The in...
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ISBN:
(数字)9781470411756
ISBN:
(纸本)9780821849491
Markov processes are among the most important stochastic processes for both theory and applications. This book develops the general theory of these processes and applies this theory to various special examples. The initial chapter is devoted to the most important classical example—one-dimensional Brownian motion. This, together with a chapter on continuous time Markov chains, provides the motivation for the general setup based on semigroups and generators. Chapters on stochastic calculus and probabilistic potential theory give an introduction to some of the key areas of application of Brownian motion and its relatives. A chapter on interacting particle systems treats a more recently developed class of Markov processes that have as their origin problems in physics and biology.
This is a textbook for a graduate course that can follow one that covers basic probabilistic limit theorems and discrete time processes.
We present a group testing approach to identify the first d vertices with the highest betweenness centrality. Betweenness centrality (BC) of a vertex is the ratio of shortest paths that pass through it and is an impor...
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ISBN:
(纸本)9781450310307
We present a group testing approach to identify the first d vertices with the highest betweenness centrality. Betweenness centrality (BC) of a vertex is the ratio of shortest paths that pass through it and is an important metric in complex networks. The Brandes algorithm computes the BC cumulatively over all vertices. Approximate BC of a single vertex can be computed by selective vertex sampling. However, applications such as community detection require only the vertices with the first few highest BC values, which are not known a-priori. In our method we sample a set of vertices and compute their combined BC. It can be shown that for small values of d, the number of tests required to find the d-highest BC vertices is logarithmic in the total number of vertices. Our algorithm is highly scalable since the samples are independently selected and therefore each test can be performed in parallel.
This book is designed to bridge the gap between traditional textbooks in statistics and more advanced books that include the sophisticated nonparametric techniques. It covers topics in parametric and nonparametric lar...
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ISBN:
(数字)9781470415938
ISBN:
(纸本)9780821852835
This book is designed to bridge the gap between traditional textbooks in statistics and more advanced books that include the sophisticated nonparametric techniques. It covers topics in parametric and nonparametric large-sample estimation theory. The exposition is based on a collection of relatively simple statistical models. It gives a thorough mathematical analysis for each of them with all the rigorous proofs and explanations. The book also includes a number of helpful exercises.
Prerequisites for the book include senior undergraduate/beginning graduate-level courses in probability and statistics.
Discrete or count data arise in experiments where the outcome variables are the numbers of individuals classified into unique, non-overlapping categories. This revised edition describes the statistical models used in ...
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ISBN:
(数字)9781383029673
ISBN:
(纸本)9780198567011
Discrete or count data arise in experiments where the outcome variables are the numbers of individuals classified into unique, non-overlapping categories. This revised edition describes the statistical models used in the analysis and summary of such data, and provides a sound introduction to the subject for graduate students and practitioners needing a review of the methodology. With many numerical examples throughout, it includes topics not covered in depth elsewhere, such as the negative multinomial distribution; the many forms of the hypergeometric distribution; and coordinate free models. A detailed treatment of sample size estimation and power are given in terms of both exact inference and asymptotic, non-central chi-squared methods. A new section covering Poisson regression has also been included. An important feature of this book, missing elsewhere, is the integration of the software into the text. Many more exercises are provided (including 84% more applied exercises) than in the previous edition, helping consolidate the reader's understanding of all subjects covered, and making the book highly suitable for use in a classroom setting. Several new datasets, mostly from the health and medical sector, are discussed, including previously unpublished data from a study of Tourette's Syndrome in children.
The book is devoted to the results on large deviations for a class of stochastic processes. Following an introduction and overview, the material is presented in three parts. Part 1 gives necessary and sufficient condi...
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ISBN:
(数字)9781470413583
ISBN:
(纸本)9781470418700
The book is devoted to the results on large deviations for a class of stochastic processes. Following an introduction and overview, the material is presented in three parts. Part 1 gives necessary and sufficient conditions for exponential tightness that are analogous to conditions for tightness in the theory of weak convergence. Part 2 focuses on Markov processes in metric spaces. For a sequence of such processes, convergence of Fleming's logarithmically transformed nonlinear semigroups is shown to imply the large deviation principle in a manner analogous to the use of convergence of linear semigroups in weak convergence. Viscosity solution methods provide applicable conditions for the necessary convergence. Part 3 discusses methods for verifying the comparison principle for viscosity solutions and applies the general theory to obtain a variety of new and known results on large deviations for Markov processes. In examples concerning infinite dimensional state spaces, new comparison principles are derived for a class of Hamilton-Jacobi equations in Hilbert spaces and in spaces of probability measures.
The summation of two harmonic voltage vectors at same frequency is only certain if their amplitudes and phase angles are well known. Therefore, there are many cases where the difference of phase angles between harmoni...
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ISBN:
(纸本)9781424472444
The summation of two harmonic voltage vectors at same frequency is only certain if their amplitudes and phase angles are well known. Therefore, there are many cases where the difference of phase angles between harmonic voltage vectors is unknown. In calculation of the steady state rating of the a.c. harmonic filter equipment, algebraic summation method is often used in determining maximal harmonic level. This summation law is very conservative as it may result in high cost of equipment ratings. Actually, a compromise should be made in taking into account the equipment safety and the risk of overrating as well as excessive costs. Based on uniform distribution of difference in phase angles, the paper provides an algorithm to calculate the probability upon which the magnitude of summation vector of two harmonic voltages may exceed a given value. This result may be applied in passive harmonic filter design in order to cut down the excessive over cost, and may be served as harmonic assessment guidance used in evaluating and setting grid power quality commitment.
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