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Exponential Families of Stochastic Processes

  • Uwe Küchler
  • Michael Sørensen

Part of the Springer Series in Statistics book series (SSS)

Table of contents

  1. Front Matter
    Pages i-x
  2. Uwe Küchler, Michael Sørensen
    Pages 1-5
  3. Uwe Küchler, Michael Sørensen
    Pages 6-17
  4. Uwe Küchler, Michael Sørensen
    Pages 19-35
  5. Uwe Küchler, Michael Sørensen
    Pages 37-43
  6. Uwe Küchler, Michael Sørensen
    Pages 45-63
  7. Uwe Küchler, Michael Sørensen
    Pages 65-79
  8. Uwe Küchler, Michael Sørensen
    Pages 81-101
  9. Uwe Küchler, Michael Sørensen
    Pages 103-134
  10. Uwe Küchler, Michael Sørensen
    Pages 135-156
  11. Uwe Küchler, Michael Sørensen
    Pages 157-204
  12. Uwe Küchler, Michael Sørensen
    Pages 205-239
  13. Uwe Küchler, Michael Sørensen
    Pages 241-266
  14. Back Matter
    Pages 267-323

About this book

Introduction

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.

Keywords

Likelihood Markov process Martingale Semimartingale Stochastic calculus Stochastic processes statistics stochastic process

Authors and affiliations

  • Uwe Küchler
    • 1
  • Michael Sørensen
    • 2
  1. 1.Institute of MathematicsHumboldt-Unversităt zu BerlinBerlinGermany
  2. 2.Institute of MathematicsAarhus UniversityAarhus CDenmark

Bibliographic information

  • DOI https://doi.org/10.1007/b98954
  • Copyright Information Springer Science+Business Media New York 1997
  • Publisher Name Springer, New York, NY
  • eBook Packages Springer Book Archive
  • Print ISBN 978-0-387-94981-9
  • Online ISBN 978-0-387-22765-8
  • Series Print ISSN 0172-7397
  • Series Online ISSN 2197-568X
  • Buy this book on publisher's site