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Stochastic processes --- Point processes --- Processus ponctuels --- 519.219 --- Processes, Point --- Random functions of several variables --- 519.219 Random functions of several variables

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Point processes and random measures find wide applicability in telecommunications, earthquakes, image analysis, spatial point patterns and stereology, to name but a few areas. The authors have made a major reshaping of their work in their first edition of 1988 and now present An Introduction to the Theory of Point Processes in two volumes with subtitles Volume I: Elementary Theory and Methods and Volume II: General Theory and Structure. Volume I contains the introductory chapters from the first edition together with an account of basic models, second order theory, and an informal account of prediction, with the aim of making the material accessible to readers primarily interested in models and applications. It also has three appendices that review the mathematical background needed mainly in Volume II. Volume II sets out the basic theory of random measures and point processes in a unified setting and continues with the more theoretical topics of the first edition: limit theorems, ergodic theory, Palm theory, and evolutionary behaviour via martingales and conditional intensity. The very substantial new material in this second volume includes expanded discussions of marked point processes, convergence to equilibrium, and the structure of spatial point processes. D.J. Daley is recently retired from the Centre for Mathematics and Applications at the Australian National University, with research publications in a diverse range of applied probability models and their analysis; he is coauthor with Joe Gani of an introductory text on epidemic modelling. The Statistical Society of Australia awarded him their Pitman Medal for 2006. D. Vere-Jones is an Emeritus Professor at Victoria University of Wellington, widely known for his contributions to Markov chains, point processes, applications in seismology, and statistical education. He is a fellow and Gold Medallist of the Royal Society of New Zealand, and a director of the consulting group Statistical Research Associates.

Point processes. --- Mathematics --- Mathematical Statistics --- Physical Sciences & Mathematics --- Processes, Point --- Mathematics. --- Probabilities. --- Probability Theory and Stochastic Processes. --- Stochastic processes --- Distribution (Probability theory. --- Distribution functions --- Frequency distribution --- Characteristic functions --- Probabilities --- Probability --- Statistical inference --- Combinations --- Chance --- Least squares --- Mathematical statistics --- Risk

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This book provides an introduction to the theory and applications of point processes, both in time and in space. Presenting the two components of point process calculus, the martingale calculus and the Palm calculus, it aims to develop the computational skills needed for the study of stochastic models involving point processes, providing enough of the general theory for the reader to reach a technical level sufficient for most applications. Classical and not-so-classical models are examined in detail, including Poisson–Cox, renewal, cluster and branching (Kerstan–Hawkes) point processes.The applications covered in this text (queueing, information theory, stochastic geometry and signal analysis) have been chosen not only for their intrinsic interest but also because they illustrate the theory. Written in a rigorous but not overly abstract style, the book will be accessible to earnest beginners with a basic training in probability but will also interest upper graduate students and experienced researchers.

Probabilities. --- Fourier analysis. --- Probability Theory and Stochastic Processes. --- Fourier Analysis. --- Analysis, Fourier --- Mathematical analysis --- Probability --- Statistical inference --- Combinations --- Mathematics --- Chance --- Least squares --- Mathematical statistics --- Risk --- Point processes. --- Processes, Point --- Stochastic processes

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Stochastic processes --- Point processes --- Analysis of variance --- Congresses --- 519.245 <063> --- Stochastic approximation. Monte Carlo methods--Congressen --- Congresses. --- 519.245 <063> Stochastic approximation. Monte Carlo methods--Congressen --- Processes, Point --- ANOVA (Analysis of variance) --- Variance analysis --- Mathematical statistics --- Experimental design --- Point processes - Congresses --- Analysis of variance - Congresses

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Stochastic processes --- Stationary processes --- Point processes --- Processus stables --- Processus ponctuels --- 519.216 --- Processes, Point --- Stochastic processes in general. Prediction theory. Stopping times. Martingales --- 519.216 Stochastic processes in general. Prediction theory. Stopping times. Martingales --- Stochastic processes. --- Processus stochastiques. --- Point processes. --- Processus ponctuels. --- Processus stochastiques --- Probabilités. --- Probabilities --- Probabilités --- Probabilities. --- Processus stationnaires