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Stochastic processes --- Point processes --- Extreme value theory --- Distribution (Probability theory) --- Processus ponctuels --- Valeurs extrêmes, Théorie des --- Distribution (Théorie des probabilités) --- 519.224 --- 519.214 --- Processes, Point --- Random variables --- Distribution functions --- Frequency distribution --- Characteristic functions --- Probabilities --- Distribution theory. Asymptotic theory. Characterization and structure theory --- Limit theorems --- Extreme value theory. --- Point processes. --- Distribution (Probability theory). --- 519.214 Limit theorems --- 519.224 Distribution theory. Asymptotic theory. Characterization and structure theory --- Valeurs extrêmes, Théorie des --- Distribution (Théorie des probabilités)

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This comprehensive text gives an interesting and useful blend of the mathematical, probabilistic and statistical tools used in heavy-tail analysis. Heavy tails are characteristic of phenomena where there is a significant probability of a single huge value impacting system behavior. Record-breaking insurance losses, financial returns, sizes of files stored on a server, transmission rates of files are all examples of heavy-tailed phenomena. Key features: Unique text devoted to heavy-tails. The treatment of heavy tails is largely dimensionless. The text gives attention to both probability modeling and statistical methods for fitting models. Most other books focus on one or the other but not both. The book emphasizes the broad applicability of heavy-tails to the fields of finance (e.g., value-at- risk), data networks, insurance. The presentation is clear, efficient and coherent and, balances theory and data analysis to show the applicability and limitations of certain methods. Several chapters examine in detail the mathematical properties of the methodologies as well as their implementation in the Splus or R statistical languages. The exposition is driven by numerous examples and exercises. Prerequisites for the reader include a prior course in stochastic processes and probability, some statistical background, some familiarity with time series analysis, and ability to use (or at least to learn) a statistics package such as R or Splus. This work will serve second-year graduate students and researchers in the areas of operations research, statistics, applied mathematics, electrical engineering, financial engineering, networking and economics. Sidney Resnick is a Professor at Cornell University and has written several well-known bestsellers: A Probability Path (ISBN: 081764055X), Adventures in Stochastic Processes (ISBN: 0817635912) and Extreme Values, Regular Variation, and Point Processes (ISBN: 0387964819).

Extreme value theory --- Distribution (Probability theory) --- Finance --- Mathematical models. --- Heavy tail analysis --- Distribution functions --- Frequency distribution --- Characteristic functions --- Probabilities --- Random variables --- Théorie des valeurs extrêmes --- Distribution (Théorie des probabilités) --- Finances --- Mathematical models --- Modèles mathématiques --- EPUB-LIV-FT Heavy LIVMATHE SPRINGER-B analysis tail --- Distribution (Probability theory. --- Mathematical statistics. --- Mathematics. --- Probability Theory and Stochastic Processes. --- Statistical Theory and Methods. --- Applications of Mathematics. --- Operations Research, Management Science. --- Mathematical Modeling and Industrial Mathematics. --- Math --- Science --- Mathematics --- Statistical inference --- Statistics, Mathematical --- Statistics --- Sampling (Statistics) --- Statistical methods --- Probabilities. --- Statistics . --- Applied mathematics. --- Engineering mathematics. --- Operations research. --- Management science. --- Models, Mathematical --- Simulation methods --- Quantitative business analysis --- Management --- Problem solving --- Operations research --- Statistical decision --- Operational analysis --- Operational research --- Industrial engineering --- Management science --- Research --- System theory --- Engineering --- Engineering analysis --- Mathematical analysis --- Statistical analysis --- Statistical data --- Statistical science --- Econometrics --- Probability --- Combinations --- Chance --- Least squares --- Mathematical statistics --- Risk --- Probabilités

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Many probability books are written by mathematicians and have the built-in bias that the reader is assumed to be a mathematician coming to the material for its beauty. This textbook is geared towards beginning graduate students from a variety of disciplines whose primary focus is not necessarily mathematics for its own sake. Instead, A Probability Path is designed for those requiring a deep understanding of advanced probability for their research in statistics, applied probability, biology, operations research, mathematical finance, and engineering.   A one-semester course is laid out in an efficient and readable manner covering the core material. The first three chapters provide a functioning knowledge of measure theory. Chapter 4 discusses independence, with expectation and integration covered in Chapter 5, followed by topics on different modes of convergence, laws of large numbers with applications to statistics (quantile and distribution function estimation), and applied probability. Two subsequent chapters offer a careful treatment of convergence in distribution and the central limit theorem. The final chapter treats conditional expectation and martingales, closing with a discussion of two fundamental theorems of mathematical finance.   Like Adventures in Stochastic Processes, Resnick’s related and very successful textbook, A Probability Path is rich in appropriate examples, illustrations, and problems, and is suitable for classroom use or self-study. The present uncorrected, softcover reprint is designed to make this classic textbook available to a wider audience.                                                             This book is different from the classical textbooks on probability theory in that it treats the measure theoretic background not as a prerequisite but as an integral part of probability theory. The result is that the reader gets a thorough and well-structured framework needed to understand the deeper concepts of current day advanced probability as it is used in statistics, engineering, biology and finance.... The pace of the book is quick and disciplined. Yet there are ample examples sprinkled over the entire book and each chapter finishes with a wealthy section of inspiring problems. —Publications of the International Statistical Institute       This textbook offers material for a one-semester course in probability, addressed to students whose primary focus is not necessarily mathematics.... Each chapter is completed by an exercises section. Carefully selected examples enlighten the reader in many situations. The book is an excellent introduction to probability and its applications. —Revue Roumaine de Mathématiques Pures et Appliquées.

Statistical science --- Mathematics --- Operational research. Game theory --- Mathematical statistics --- Probability theory --- Planning (firm) --- toegepaste wiskunde --- waarschijnlijkheidstheorie --- stochastische analyse --- mathematische modellen --- statistiek --- econometrie --- wiskunde --- operationeel onderzoek --- kansrekening --- statistisch onderzoek

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This comprehensive text gives an interesting and useful blend of the mathematical, probabilistic and statistical tools used in heavy-tail analysis. Heavy tails are characteristic of phenomena where there is a significant probability of a single huge value impacting system behavior. Record-breaking insurance losses, financial returns, sizes of files stored on a server, transmission rates of files are all examples of heavy-tailed phenomena. Key features: Unique text devoted to heavy-tails. The treatment of heavy tails is largely dimensionless. The text gives attention to both probability modeling and statistical methods for fitting models. Most other books focus on one or the other but not both. The book emphasizes the broad applicability of heavy-tails to the fields of finance (e.g., value-at- risk), data networks, insurance. The presentation is clear, efficient and coherent and, balances theory and data analysis to show the applicability and limitations of certain methods. Several chapters examine in detail the mathematical properties of the methodologies as well as their implementation in the Splus or R statistical languages. The exposition is driven by numerous examples and exercises. Prerequisites for the reader include a prior course in stochastic processes and probability, some statistical background, some familiarity with time series analysis, and ability to use (or at least to learn) a statistics package such as R or Splus. This work will serve second-year graduate students and researchers in the areas of operations research, statistics, applied mathematics, electrical engineering, financial engineering, networking and economics. Sidney Resnick is a Professor at Cornell University and has written several well-known bestsellers: A Probability Path (ISBN: 081764055X), Adventures in Stochastic Processes (ISBN: 0817635912) and Extreme Values, Regular Variation, and Point Processes (ISBN: 0387964819).

Statistical science --- Operational research. Game theory --- Mathematics --- Planning (firm) --- toegepaste wiskunde --- stochastische analyse --- mathematische modellen --- speltheorie --- operationeel onderzoek --- kansrekening --- statistisch onderzoek

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A Lévy process is a continuous-time analogue of a random walk, and as such, is at the cradle of modern theories of stochastic processes. Martingales, Markov processes, and diffusions are extensions and generalizations of these processes. In the past, representatives of the Lévy class were considered most useful for applications to either Brownian motion or the Poisson process. Nowadays the need for modeling jumps, bursts, extremes and other irregular behavior of phenomena in nature and society has led to a renaissance of the theory of general Lévy processes. Researchers and practitioners in fields as diverse as physics, meteorology, statistics, insurance, and finance have rediscovered the simplicity of Lévy processes and their enormous flexibility in modeling tails, dependence and path behavior. This volume, with an excellent introductory preface, describes the state-of-the-art of this rapidly evolving subject with special emphasis on the non-Brownian world. Leading experts present surveys of recent developments, or focus on some most promising applications. Despite its special character, every topic is aimed at the non- specialist, keen on learning about the new exciting face of a rather aged class of processes. An extensive bibliography at the end of each article makes this an invaluable comprehensive reference text. For the researcher and graduate student, every article contains open problems and points out directions for futurearch. The accessible nature of the work makes this an ideal introductory text for graduate seminars in applied probability, stochastic processes, physics, finance, and telecommunications, and a unique guide to the world of Lévy processes. .

Stochastic processes --- Lévy processes. --- Lévy processes --- 519.282 --- Random walks (Mathematics) --- Probabilities. --- Applied mathematics. --- Engineering mathematics. --- Operations research. --- Management science. --- Probability Theory and Stochastic Processes. --- Applications of Mathematics. --- Operations Research, Management Science. --- Quantitative business analysis --- Management --- Problem solving --- Operations research --- Statistical decision --- Operational analysis --- Operational research --- Industrial engineering --- Management science --- Research --- System theory --- Engineering --- Engineering analysis --- Mathematical analysis --- Probability --- Statistical inference --- Combinations --- Mathematics --- Chance --- Least squares --- Mathematical statistics --- Risk