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Written by two of the leading researchers in the field, this will be the first book-treatment of the literature on exponential families of stochastic processes. It will be of interest to theoretical statisticians and probabilists.
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A comprehensive account of the statistical theory of exponential families of stochastic processes. The book reviews the progress in the field made over the last ten years or so by the authors - two of the leading experts in the field - and several other researchers. The theory is applied to a broad spectrum of examples, covering a large number of frequently applied stochastic process models with discrete as well as continuous time. To make the reading even easier for statisticians with only a basic background in the theory of stochastic process, the first part of the book is based on classical theory of stochastic processes only, while stochastic calculus is used later. Most of the concepts and tools from stochastic calculus needed when working with inference for stochastic processes are introduced and explained without proof in an appendix. This appendix can also be used independently as an introduction to stochastic calculus for statisticians. Numerous exercises are also included.
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Exponential Families of Stochastic Processes (Springer Series in Statistics)
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Exponential Families of Stochastic Processes
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Exponential Families of Stochastic Processes (Paperback)
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Springer-Verlag New York Inc., New York, NY, 2013
ISBN 10: 1475771002
ISBN 13: 9781475771008
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Paperback. Zustand: new. Paperback. Exponential families of stochastic processes are parametric stochastic p- cess models for which the likelihood function exists at all ?nite times and has an exponential representation where the dimension of the canonical statistic is ?nite and independent of time. This de?nition not only covers manypracticallyimportantstochasticprocessmodels,italsogivesrisetoa rather rich theory. This book aims at showing both aspects of exponential families of stochastic processes. Exponential families of stochastic processes are tractable from an a- lytical as well as a probabilistic point of view. Therefore, and because the theory covers many important models, they form a good starting point for an investigation of the statistics of stochastic processes and cast interesting light on basic inference problems for stochastic processes. Exponential models play a central role in classical statistical theory for independent observations, where it has often turned out to be informative and advantageous to view statistical problems from the general perspective of exponential families rather than studying individually speci?c expon- tial families of probability distributions. The same is true of stochastic process models. Thus several published results on the statistics of parti- lar process models can be presented in a uni?ed way within the framework of exponential families of stochastic processes. Exponential families of stochastic processes are parametric stochastic p- cess models for which the likelihood function exists at all ?nite times and has an exponential representation where the dimension of the canonical statistic is ?nite and independent of time. Shipping may be from multiple locations in the US or from the UK, depending on stock availability. Bestandsnummer des Verkäufers 9781475771008
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Exponential Families of Stochastic Processes
Verlag:
Springer-Verlag New York Inc., 2013
ISBN 10: 1475771002
ISBN 13: 9781475771008
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