Fluctuations of Levy Processes with Applications, Kyprianou, Andreas E.

Автор: Liptser Robert S., Shiryaev Albert N., Aries A.B.
Название: Statistics of Random Processes / II. Applications
ISBN: 3540639284 ISBN-13(EAN): 9783540639282
Издательство: Springer
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Описание: The subject of these two volumes is non-linear filtering (prediction and smoothing) theory and its application to the problem of optimal estimation, control with incomplete data, information theory, and sequential testing of hypothesis. The book is not only addressed to mathematicians but should also serve the interests of other scientists who apply probabilistic and statistical methods in their work. The theory of martingales presented in the book has an independent interest in connection with problems from financial mathematics. In the second edition, the authors have made numerous corrections, updating every chapter, adding two new subsections devoted to the Kalman filter under wrong initial conditions, as well as a new chapter devoted to asymptotically optimal filtering under diffusion approximation. Moreover, in each chapter a comment is added about the progress of recent years.

Автор: del Puerto
Название: Branching Processes and Their Applications
ISBN: 3319316397 ISBN-13(EAN): 9783319316390
Издательство: Springer
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Цена: 15372.00 р.
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Описание: This volume gathers papers originally presented at the 3rd Workshop on Branching Processes and their Applications (WBPA15), which was held from 7 to 10 April 2015 in Badajoz, Spain (http://branching.unex.es/wbpa15/index.htm).

Автор: Phadia
Название: Prior Processes and Their Applications
ISBN: 3319327887 ISBN-13(EAN): 9783319327884
Издательство: Springer
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Описание: This book presents a systematic and comprehensive treatment of various prior processes that have been developed over the past four decades for dealing with Bayesian approach to solving selected nonparametric inference problems. This revised edition has been substantially expanded to reflect the current interest in this area. After an overview of different prior processes, it examines the now pre-eminent Dirichlet process and its variants including hierarchical processes, then addresses new processes such as dependent Dirichlet, local Dirichlet, time-varying and spatial processes, all of which exploit the countable mixture representation of the Dirichlet process. It subsequently discusses various neutral to right type processes, including gamma and extended gamma, beta and beta-Stacy processes, and then describes the Chinese Restaurant, Indian Buffet and infinite gamma-Poisson processes, which prove to be very useful in areas such as machine learning, information retrieval and featural modeling. Tailfree and Polya tree and their extensions form a separate chapter, while the last two chapters present the Bayesian solutions to certain estimation problems pertaining to the distribution function and its functional based on complete data as well as right censored data. Because of the conjugacy property of some of these processes, most solutions are presented in closed form. However, the current interest in modeling and treating large-scale and complex data also poses a problem – the posterior distribution, which is essential to Bayesian analysis, is invariably not in a closed form, making it necessary to resort to simulation. Accordingly, the book also introduces several computational procedures, such as the Gibbs sampler, Blocked Gibbs sampler and slice sampling, highlighting essential steps of algorithms while discussing specific models. In addition, it features crucial steps of proofs and derivations, explains the relationships between different processes and provides further clarifications to promote a deeper understanding. Lastly, it includes a comprehensive list of references, equipping readers to explore further on their own.

Автор: Vicsek, Tamas
Название: Fluctuations and Scaling in Biology (Paperback)
ISBN: 0198507909 ISBN-13(EAN): 9780198507901
Издательство: Oxford Academ
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Цена: 11563.00 р.
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Описание: During the last decade the well established tools of statistical physics have been sucessfully appled to an increasing number of biological phenomena, including fractal pattern formation, group motion in organisms from bacteria to humans, and the mechanisms by which fluctuations are rectified in the cells molecular machinery.