Overview
- Authors:
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Uwe Küchler
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Institute of Mathematics, Humboldt-Unversităt zu Berlin, Berlin, Germany
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Michael Sørensen
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Institute of Mathematics, Aarhus University, Aarhus C, Denmark
- The first book to cover exponential families of stochastic processes *
- The statistical concepts are explained carefully so that probabilists with only a basic background in statistics can use the book to get into statistical inference for stochastic processes
- Includes many results from the authors' progress in the field
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Table of contents (12 chapters)
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- Uwe Küchler, Michael Sørensen
Pages 1-5
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- Uwe Küchler, Michael Sørensen
Pages 6-17
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- Uwe Küchler, Michael Sørensen
Pages 19-35
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- Uwe Küchler, Michael Sørensen
Pages 37-43
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- Uwe Küchler, Michael Sørensen
Pages 45-63
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- Uwe Küchler, Michael Sørensen
Pages 65-79
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- Uwe Küchler, Michael Sørensen
Pages 81-101
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- Uwe Küchler, Michael Sørensen
Pages 103-134
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- Uwe Küchler, Michael Sørensen
Pages 135-156
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- Uwe Küchler, Michael Sørensen
Pages 157-204
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- Uwe Küchler, Michael Sørensen
Pages 205-239
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- Uwe Küchler, Michael Sørensen
Pages 241-266
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Back Matter
Pages 267-323
About this book
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.
Authors and Affiliations
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Institute of Mathematics, Humboldt-Unversităt zu Berlin, Berlin, Germany
Uwe Küchler
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Institute of Mathematics, Aarhus University, Aarhus C, Denmark
Michael Sørensen
