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Mathematical statistics --- Sufficient statistics --- Distribution (Probability theory) --- Exponential functions --- 519.24 --- 519.221 --- Statistics, Sufficient --- Sampling (Statistics) --- Functions, Exponential --- Hyperbolic functions --- Exponents (Algebra) --- Logarithms --- Transcendental functions --- Distribution functions --- Frequency distribution --- Characteristic functions --- Probabilities --- Special statistical applications and models --- Foundations of statistical theory --- 519.221 Foundations of statistical theory --- 519.24 Special statistical applications and models

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Drawing on advanced probability theory, Ambit Stochastics is used to model stochastic processes which depend on both time and space. This monograph, the first on the subject, provides a reference for this burgeoning field, complete with the applications that have driven its development. Unique to Ambit Stochastics are ambit sets, which allow the delimitation of space-time to a zone of interest, and ambit fields, which are particularly well-adapted to modelling stochastic volatility or intermittency. These attributes lend themselves notably to applications in the statistical theory of turbulence and financial econometrics. In addition to the theory and applications of Ambit Stochastics, the book also contains new theory on the simulation of ambit fields and a comprehensive stochastic integration theory for Volterra processes in a non-semimartingale context. Written by pioneers in the subject, this book will appeal to researchers and graduate students interested in empirical stochastic modelling.

Statistical science --- Finance --- Operational research. Game theory --- Mathematical statistics --- Probability theory --- Mathematics --- Mathematical physics --- Business economics --- financieel management --- waarschijnlijkheidstheorie --- stochastische analyse --- statistiek --- financiën --- econometrie --- wiskunde --- fysica --- kansrekening --- statistisch onderzoek --- Distribution (Probability theory. --- Finance. --- Statistics. --- Probability Theory and Stochastic Processes. --- Mathematical Applications in the Physical Sciences. --- Quantitative Finance. --- Mathematical Physics. --- Statistics for Business, Management, Economics, Finance, Insurance. --- Statistics for Engineering, Physics, Computer Science, Chemistry and Earth Sciences. --- Statistical analysis --- Statistical data --- Statistical methods --- Econometrics --- Funding --- Funds --- Economics --- Currency question --- Distribution functions --- Frequency distribution --- Characteristic functions --- Probabilities --- Probabilities. --- Mathematical physics. --- Economics, Mathematical . --- Statistics . --- Mathematical economics --- Physical mathematics --- Physics --- Probability --- Statistical inference --- Combinations --- Chance --- Least squares --- Risk --- Methodology

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Asymptotic theory --- -519.214 --- Limit theorems --- Asymptotic theory. --- 519.214 Limit theorems --- Théorie asymptotique --- Mathematical statistics --- 519.214 --- Asymptotic expansions --- Statistique mathématique --- Échantillonnage (statistique) --- Sampling (Statistics) --- Statistique mathématique --- Théorie asymptotique --- Mathematical statistics - Asymptotic theory --- Statistique mathématique. --- Échantillonnage (statistique)

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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