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This volume is devoted to the study of asymptotic properties of wide classes of stochastic systems arising in mathematical statistics, percolation theory, statistical physics and reliability theory. Attention is paid not only to positive and negative associations introduced in the pioneering papers by Harris, Lehmann, Esary, Proschan, Walkup, Fortuin, Kasteleyn and Ginibre, but also to new and more general dependence conditions. Naturally, this scope comprises families of independent real-valued random variables. A variety of important results and examples of Markov processes, random measures

Random fields. --- Limit theorems (Probability theory) --- Probabilities --- Fields, Random --- Stochastic processes --- Random fields --- Champs aléatoires --- Théorèmes limites (Théorie des probabilités)

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Randomized algorithms have become a central part of the algorithms curriculum, based on their increasingly widespread use in modern applications. This book presents a coherent and unified treatment of probabilistic techniques for obtaining high probability estimates on the performance of randomized algorithms. It covers the basic toolkit from the Chernoff-Hoeffding bounds to more sophisticated techniques like martingales and isoperimetric inequalities, as well as some recent developments like Talagrand's inequality, transportation cost inequalities and log-Sobolev inequalities. Along the way, variations on the basic theme are examined, such as Chernoff-Hoeffding bounds in dependent settings. The authors emphasise comparative study of the different methods, highlighting respective strengths and weaknesses in concrete example applications. The exposition is tailored to discrete settings sufficient for the analysis of algorithms, avoiding unnecessary measure-theoretic details, thus making the book accessible to computer scientists as well as probabilists and discrete mathematicians.

Random variables. --- Distribution (Probability theory) --- Limit theorems (Probability theory) --- Algorithms. --- Algorism --- Algebra --- Arithmetic --- Probabilities --- Distribution functions --- Frequency distribution --- Characteristic functions --- Chance variables --- Stochastic variables --- Variables (Mathematics) --- Foundations

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The subject of this book lies on the boundary between probability theory and the theory of function spaces. Here Professor Braverman investigates independent random variables in rearrangement invariant (r.i.) spaces. The significant feature of r.i. spaces is that the norm of an element depends on its distribution only, and this property allows the results and methods associated with r.i. spaces to be applied to problems in probability theory. On the other hand, probabilistic methods can also prove useful in the study of r.i. spaces. In this book new techniques are used and a number of interesting results are given. Most of the results are due to the author but have never before been available in English. Here they are all presented together in a volume that will be essential reading for all serious researchers in this area.

Random variables. --- Rearrangement invariant spaces. --- Inequalities (Mathematics) --- Processes, Infinite --- Invariant spaces, Rearrangement --- Spaces, Rearrangement invariant --- Function spaces --- Chance variables --- Stochastic variables --- Probabilities --- Variables (Mathematics) --- Probability --- Random variables --- Rearrangement invariant spaces --- Variables aléatoires --- Sous espaces invariants --- 519.214 --- 519.214 Limit theorems --- Limit theorems

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The theory of large deviations deals with the evaluation, for a family of probability measures parameterized by a real valued variable, of the probabilities of events which decay exponentially in the parameter. Originally developed in the context of statistical mechanics and of (random) dynamical systems, it proved to be a powerful tool in the analysis of systems where the combined effects of random perturbations lead to a behavior significantly different from the noiseless case. The volume complements the central elements of this theory with selected applications in communication and control systems, bio-molecular sequence analysis, hypothesis testing problems in statistics, and the Gibbs conditioning principle in statistical mechanics. Starting with the definition of the large deviation principle (LDP), the authors provide an overview of large deviation theorems in ${{m I!R}}^d$ followed by their application. In a more abstract setup where the underlying variables take values in a topological space, the authors provide a collection of methods aimed at establishing the LDP, such as transformations of the LDP, relations between the LDP and Laplace's method for the evaluation for exponential integrals, properties of the LDP in topological vector spaces, and the behavior of the LDP under projective limits. They then turn to the study of the LDP for the sample paths of certain stochastic processes and the application of such LDP's to the problem of the exit of randomly perturbed solutions of differential equations from the domain of attraction of stable equilibria. They conclude with the LDP for the empirical measure of (discrete time) random processes: Sanov's theorem for the empirical measure of an i.i.d. sample, its extensions to Markov processes and mixing sequences and their application. The present soft cover edition is a corrected printing of the 1998 edition. Amir Dembo is a Professor of Mathematics and of Statistics at Stanford University. Ofer Zeitouni is a Professor of Mathematics at the Weizmann Institute of Science and at the University of Minnesota.

Electronic books. -- local. --- Large deviations. --- Limit theorems (Probability theory). --- Civil & Environmental Engineering --- Operations Research --- Engineering & Applied Sciences --- Limit theorems (Probability theory) --- Deviations, Large --- Mathematics. --- System theory. --- Probabilities. --- Systems Theory, Control. --- Probability Theory and Stochastic Processes. --- Probabilities --- Statistics --- Systems theory. --- Distribution (Probability theory. --- Distribution functions --- Frequency distribution --- Characteristic functions --- Probability --- Statistical inference --- Combinations --- Mathematics --- Chance --- Least squares --- Mathematical statistics --- Risk --- Systems, Theory of --- Systems science --- Science --- Philosophy

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This volume is dedicated to the memory of the late Professor C.C. (Chris) Heyde (1939-2008), distinguished statistician, mathematician and scientist. Chris worked at a time when many of the foundational building blocks of probability and statistics were being put in place by a phalanx of eminent scientists around the world. He contributed significantly to this effort and took his place deservedly among the top-most rank of researchers. Throughout his career, Chris maintained also a keen interest in applications of probability and statistics, and in the history of the subject. The magnitude of his impact on his chosen area of research, both in Australia and internationally, was well recognised by the abundance of honours he received within and without the profession. The book is comprised of a number of Chris’s papers covering each one of four major topics to which he contributed. These papers are reproduced herein. The topics, and the papers in them, were selected by four of Chris’s friends and collaborators: Ishwar Basawa, Peter Hall, Ross Maller (overall Editor of the volume) and Eugene Seneta. Each topic is provided with an overview by the selecting editor. The topics cover a range of areas to which Chris made especially important contributions: Inference in Stochastic Processes, Rates of Convergence in the Central Limit Theorem, the Law of the Iterated Logarithm, and Branching Processes and Population Genetics. The Editor and the other contributors to the volume include well known researchers in probability and statistics. The collection begins with an “author’s pick” of a number of his papers which Chris considered most interesting and significant, chosen by him shortly before his death. A biography of Chris by his close friend and collaborator, Joe Gani, is also included. An introduction by the Editor and a comprehensive bibliography of Chris’s publications complete the volume. The book will be of especial interest to researchers in probability and statistics, and in the history of these subjects.

Branching processes. --- Limit theorems (Probability theory). --- Mathematical statistics. --- Probabilities. --- Stochastic processes. --- Mathematical statistics --- Probabilities --- Stochastic processes --- Branching processes --- Limit theorems (Probability theory) --- Mathematics --- Physical Sciences & Mathematics --- Mathematical Statistics --- Random processes --- Probability --- Statistical inference --- Statistics. --- Economics, Mathematical. --- Biomathematics. --- Econometrics. --- Statistical Theory and Methods. --- Probability Theory and Stochastic Processes. --- Mathematical and Computational Biology. --- Quantitative Finance. --- Combinations --- Chance --- Least squares --- Risk --- Distribution (Probability theory. --- Finance. --- Funding --- Funds --- Economics --- Currency question --- Economics, Mathematical --- Statistics --- Distribution functions --- Frequency distribution --- Characteristic functions --- Statistics, Mathematical --- Sampling (Statistics) --- Statistical methods --- Statistics . --- Economics, Mathematical . --- Mathematical economics --- Econometrics --- Biology --- Statistical analysis --- Statistical data --- Statistical science --- Methodology