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A one-year course in probability theory and the theory of random processes, taught at Princeton University to undergraduate and graduate students, forms the core of the content of this book It is structured in two parts: the first part providing a detailed discussion of Lebesgue integration, Markov chains, random walks, laws of large numbers, limit theorems, and their relation to Renormalization Group theory. The second part includes the theory of stationary random processes, martingales, generalized random processes, Brownian motion, stochastic integrals, and stochastic differential equations. One section is devoted to the theory of Gibbs random fields. This material is essential to many undergraduate and graduate courses. The book can also serve as a reference for scientists using modern probability theory in their research.

Probabilities. --- Stochastic processes. --- Probability --- Statistical inference --- Combinations --- Mathematics --- Chance --- Least squares --- Mathematical statistics --- Risk --- Random processes --- Probabilities --- Distribution (Probability theory. --- Probability Theory and Stochastic Processes. --- Distribution functions --- Frequency distribution --- Characteristic functions

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Soils and rocks are among the most variable of all engineering materials, and as such are highly amenable to a probabilistic treatment. The application of statistical and probabilistic concepts to geotechnical analysis is a rapidly growing area of interest for both academics and practitioners. The book is therefore aimed at students, researchers, and practitioners of geotechnical engineering who wish to keep abreast of developments in this evolving field of study. The course content and will assume no more that an introductory understanding of probability and statistics on the part of the course participants. The main objective is to present a state-of-the-art training on probabilistic techniques applied to geotechnical engineering in relation to both theory and practice. Including: (a) discussion of potential benefits of probabilistic approaches as opposed to the classical “Factor of Safety” methods, to review sources of uncertainty in geotechnical analysis and to introduce methods of LRFD and reliability concepts in Eurocode 7, (b) review of relevant statistical theories needed to develop the methodologies and interpret the results of probabilistic analysis, (c) examples of established probabilistic methods of analysis in geotechnical engineering, such as the First Order Second Moment (FOSM) method, the Point Estimate Method (PEM), the First and Second Order Reliability Methods (FORM SORM) and Random Set (RS) theory, (d) description of numerical methods of probabilistic analysis based on the finite element method, such as the Stochastic Finite Element Method (SFEM) and recent developments on the Random Finite Element Method (RFEM), (e) practical examples and case histories of probabilistic applications in geotechnical engineering.

Soil mechanics --- Probabilities. --- Statistical methods. --- Probability --- Statistical inference --- Combinations --- Mathematics --- Chance --- Least squares --- Mathematical statistics --- Risk --- Soil engineering --- Soils --- Soils (Engineering) --- Geotechnical engineering --- Mechanics --- Foundations --- Soil physics --- Civil engineering. --- Distribution (Probability theory. --- Geotechnical Engineering & Applied Earth Sciences. --- Civil Engineering. --- Probability Theory and Stochastic Processes. --- Distribution functions --- Frequency distribution --- Characteristic functions --- Probabilities --- Engineering --- Public works --- Geotechnical engineering. --- Engineering, Geotechnical --- Geotechnics --- Geotechnology --- Engineering geology

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"At last, after a decade of mounting interest in log-linear and related models for the analysis of discrete multivariate data, particularly in the form of multidimensional tables, we now have a comprehensive text and general reference on the subject. Even a mediocre attempt to organize the extensive and widely scattered literature on discrete multivariate analysis would be welcome; happily, this is an excellent such effort, but a group of Harvard statisticians that has contributed much to the field. Their book ought to serve as a basic guide to the analysis of quantitative data for years to come." --James R. Beninger, Contemporary Sociology "A welcome addition to multivariate analysis. The discussion is lucid and very leisurely, excellently illustrated with applications drawn from a wide variety of fields. A good part of the book can be understood without very specialized statistical knowledge. It is a most welcome contribution to an interesting and lively subject." --D.R. Cox, Nature "Discrete Multivariate Analysis is an ambitious attempt to present log-linear models to a broad audience. Exposition is quite discursive, and the mathematical level, except in Chapters 12 and 14, is very elementary. To illustrate possible applications, some 60 different sets of data have been gathered together from diverse fields. To aid the reader, an index of these examples has been provided. ...the book contains a wealth of material on important topics. Its numerous examples are especially valuable." --Shelby J. Haberman, The Annals of Statistics.

Mathematics. --- Probabilities. --- Statistics. --- Probability Theory and Stochastic Processes. --- Statistical Theory and Methods. --- Statistical analysis --- Statistical data --- Statistical methods --- Statistical science --- Mathematics --- Econometrics --- Probability --- Statistical inference --- Combinations --- Chance --- Least squares --- Mathematical statistics --- Risk --- Math --- Science --- Distribution (Probability theory. --- Mathematical statistics. --- Statistics, Mathematical --- Statistics --- Probabilities --- Sampling (Statistics) --- Distribution functions --- Frequency distribution --- Characteristic functions --- Statistics .

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The book develops the necessary background in probability theory underlying diverse treatments of stochastic processes and their wide-ranging applications. With this goal in mind, the pace is lively, yet thorough. Basic notions of independence and conditional expectation are introduced relatively early on in the text, while conditional expectation is illustrated in detail in the context of martingales, Markov property and strong Markov property. Weak convergence of probabilities on metric spaces and Brownian motion are two highlights. The historic role of size-biasing is emphasized in the contexts of large deviations and in developments of Tauberian Theory. The authors assume a graduate level of maturity in mathematics, but otherwise the book will be suitable for students with varying levels of background in analysis and measure theory. In particular, theorems from analysis and measure theory used in the main text are provided in comprehensive appendices, along with their proofs, for ease of reference. Rabi Bhattacharya is Professor of Mathematics at the University of Arizona. Edward Waymire is Professor of Mathematics at Oregon State University. Both authors have co-authored numerous books, including the graduate textbook, Stochastic Processes with Applications.

Mathematics. --- Probabilities. --- Probability --- Statistical inference --- Combinations --- Mathematics --- Chance --- Least squares --- Mathematical statistics --- Risk --- Math --- Science --- Distribution (Probability theory. --- Global analysis (Mathematics). --- Probability Theory and Stochastic Processes. --- Measure and Integration. --- Analysis. --- Analysis, Global (Mathematics) --- Differential topology --- Functions of complex variables --- Geometry, Algebraic --- Distribution functions --- Frequency distribution --- Characteristic functions --- Probabilities --- Measure theory. --- Mathematical analysis. --- Analysis (Mathematics). --- Lebesgue measure --- Measurable sets --- Measure of a set --- Algebraic topology --- Integrals, Generalized --- Measure algebras --- Rings (Algebra) --- 517.1 Mathematical analysis --- Mathematical analysis

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Lévy processes, i.e. processes in continuous time with stationary and independent increments, are named after Paul Lévy, who made the connection with infinitely divisible distributions and described their structure. They form a flexible class of models, which have been applied to the study of storage processes, insurance risk, queues, turbulence, laser cooling, ... and of course finance, where the feature that they include examples having "heavy tails" is particularly important. Their sample path behaviour poses a variety of difficult and fascinating problems. Such problems, and also some related distributional problems, are addressed in detail in these notes that reflect the content of the course given by R. Doney in St. Flour in 2005.

Lévy processes. --- Lévy, Processus de --- Electronic books. -- local. --- Lévy processes. --- Random walks (Mathematics). --- Lâevy processes --- Mathematics --- Physical Sciences & Mathematics --- Mathematical Theory --- Mathematical Statistics --- Random walks (Mathematics) --- Lévy, Processus de --- EPUB-LIV-FT SPRINGER-B --- Additive process (Probability theory) --- Random walk process (Mathematics) --- Walks, Random (Mathematics) --- Mathematics. --- Probabilities. --- Probability Theory and Stochastic Processes. --- Probability --- Statistical inference --- Combinations --- Chance --- Least squares --- Mathematical statistics --- Risk --- Math --- Science --- Stochastic processes --- Distribution (Probability theory. --- Distribution functions --- Frequency distribution --- Characteristic functions --- Probabilities