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Exponential Families of Stochastic Processes : Springer Series in Statistics - U. Kuchler

Exponential Families of Stochastic Processes

Springer Series in Statistics

Hardcover Published: 10th July 1997
ISBN: 9780387949819
Number Of Pages: 322

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This is author-approved bcc: This book provides 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. A large number of frequently applied stochastic process models with discrete as well as with continuous time are covered by the theory developed in the book. The exponential families of stochastic processes are the most tractable type of statistical models for stochastic processes. On the other hand, they include models that are complex enough to exhibit basic inference problems that are peculiar to stochastic process models. Therefore they are a good starting point for the statistican who plans to work in this interesting and vigorous field. To make the reading 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 late in the book. Most of the concepts and tools from stochastic calculus that a statistician is likely to need, when working with inference for stochastic processes, are introduced and explained without proof in an appendix. The appendix can also be used independently as an introduction to stochastic calculus for statisticians. 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. Exercises are included to make the book useful for an advanced

Preface
Introductionp. 1
Natural Exponential Families of Levy Processesp. 7
Definitions and Examplesp. 19
First Propertiesp. 37
Random Time Transformationsp. 45
Exponential Families of Markov Processesp. 65
The Envelope Familiesp. 81
Likelihood Theoryp. 103
Linear Stochastic Differential Equations with Time Delayp. 135
Sequential Methodsp. 157
The Semimartingale Approachp. 205
Alternative Definitionsp. 241
A Toolbox from Stochastic Calculusp. 267
Miscellaneous Resultsp. 299
C: Referencesp. 303
Basic Notationp. 317
Indexp. 319
Table of Contents provided by Blackwell. All Rights Reserved.

ISBN: 9780387949819
ISBN-10: 038794981X
Series: Springer Series in Statistics
Audience: Professional
Format: Hardcover
Language: English
Number Of Pages: 322
Published: 10th July 1997
Publisher: Springer-Verlag New York Inc.
Country of Publication: US
Dimensions (cm): 24.77 x 16.51  x 2.54
Weight (kg): 0.61

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