Ole E. Barndorff-Nielsen

Shun'ichi Amari

R.E. Kass

S.L. Lauritzen

C.R. Rao

Differential Geometry in Statistical Inference

David Applebaum

"This series reports on new developments in mathematical research and teaching - quickly, informally and at a high level. The type of material considered for publication includes: research monographs; lectures on a new field or presentations of a new angle in a classical field; and summer schools and intensive courses on topics of current research."--BOOK JACKET.

Structure of Quantum Lévy Processes, Classical Probability, and Physics

Quantum Independent Increment Processes II

Al?bert Nikolaevich Shiri?a?ev

A comprehensive account of two topics that are of particular significance in both theoretical and applied stochastics: random change of time and change of probability law. The book comprehensively collects and integrates results from a number of scattered sources in the literature and discusses the importance of the results.

Change of Time and Change of Measure

On Conditional Inference for Deviation from Hardy-Weinberg Distribution

Brian B. Willetts

Aeolian Grain Transport: Mechanics

Fred Espen Benth

Almut E. D. Veraart

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.

Ambit Stochastics

Sidney I. Resnick

Thomas Mikosch

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.

Theory and Applications

Lévy Processes

Ole E. Barndorff-Nielsen

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