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Infinitely Divisible Statistical Experiments

  • Book
  • © 1985

Overview

Authors:
  1. Arnold Janssen

    1. Fachbereich 6 — Mathematik, Universität-Gesamthochschule-Siegen, Siegen, Federal Republic of Germany

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  2. Hartmut Milbrodt

    1. Mathematik VII, Universität Bayreuth, Bayreuth, Federal Republic of Germany

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  3. Helmut Strasser

    1. Mathematik VII, Universität Bayreuth, Bayreuth, Federal Republic of Germany

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Part of the book series: Lecture Notes in Statistics (LNS, volume 27)

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Table of contents (20 chapters)

  1. Front Matter

    Pages N2-VI
    Download chapter PDF

  2. Introduction

    1. Introduction

      • Arnold Janssen, Hartmut Milbrodt, Helmut Strasser
      Pages 1-13

  3. Limits of Triangular Arrays of Experiments

    1. Basic Concepts

      • Arnold Janssen, Hartmut Milbrodt, Helmut Strasser
      Pages 14-18

    2. Gaussian Experiments

      • Arnold Janssen, Hartmut Milbrodt, Helmut Strasser
      Pages 19-24

    3. Introduction to Poisson Experiments

      • Arnold Janssen, Hartmut Milbrodt, Helmut Strasser
      Pages 25-31

    4. Convergence of Poisson Experiments

      • Arnold Janssen, Hartmut Milbrodt, Helmut Strasser
      Pages 32-37

    5. Convergence of Triangular Arrays

      • Arnold Janssen, Hartmut Milbrodt, Helmut Strasser
      Pages 38-46

    6. Identification of Limit Experiments

      • Arnold Janssen, Hartmut Milbrodt, Helmut Strasser
      Pages 47-54

  4. The Lévy-Khintchine Formula for Infinitely Divisible Statistical Experiments

    1. Preliminaries

      • Arnold Janssen, Hartmut Milbrodt, Helmut Strasser
      Pages 55-57

    2. Infinitely Divisible Probability Measures

      • Arnold Janssen, Hartmut Milbrodt, Helmut Strasser
      Pages 58-62

    3. The Lévy-Khintchine Formula for Standard Measures

      • Arnold Janssen, Hartmut Milbrodt, Helmut Strasser
      Pages 63-88

    4. The Lévy-Khintchine Formula for Arbitrary Regular Infinitely Divisible Statistical Experiments

      • Arnold Janssen, Hartmut Milbrodt, Helmut Strasser
      Pages 89-105

  5. Representation of Poisson Experiments

    1. Generalized Poisson Processes

      • Arnold Janssen, Hartmut Milbrodt, Helmut Strasser
      Pages 106-110

    2. Standard Poisson Experiments

      • Arnold Janssen, Hartmut Milbrodt, Helmut Strasser
      Pages 111-123

  6. Statistical Experiments with Independent Increments

    1. Preliminaries

      • Arnold Janssen, Hartmut Milbrodt, Helmut Strasser
      Pages 124-125

    2. Experiments with Independent Increments

      • Arnold Janssen, Hartmut Milbrodt, Helmut Strasser
      Pages 126-129

    3. Existence and Construction of Experiments with Independent Increments

      • Arnold Janssen, Hartmut Milbrodt, Helmut Strasser
      Pages 130-132

    4. Infinitely Divisible Experiments with Independent Increments

      • Arnold Janssen, Hartmut Milbrodt, Helmut Strasser
      Pages 133-139

    5. Weak Convergence of Triangular Arrays to Experiments with Independent Increments

      • Arnold Janssen, Hartmut Milbrodt, Helmut Strasser
      Pages 140-143

    6. The Likelihood Process

      • Arnold Janssen, Hartmut Milbrodt, Helmut Strasser
      Pages 144-148
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Keywords

Authors and Affiliations

  • Fachbereich 6 — Mathematik, Universität-Gesamthochschule-Siegen, Siegen, Federal Republic of Germany

    Arnold Janssen

  • Mathematik VII, Universität Bayreuth, Bayreuth, Federal Republic of Germany

    Hartmut Milbrodt, Helmut Strasser

Bibliographic Information

  • Book Title: Infinitely Divisible Statistical Experiments

  • Authors: Arnold Janssen, Hartmut Milbrodt, Helmut Strasser

  • Series Title: Lecture Notes in Statistics

  • DOI: https://doi.org/10.1007/978-1-4615-7261-9

  • Publisher: Springer New York, NY

  • eBook Packages: Springer Book Archive

  • Copyright Information: Springer-Verlag Berlin Heidelberg 1985

  • Softcover ISBN: 978-0-387-96055-5Published: 06 May 1985

  • eBook ISBN: 978-1-4615-7261-9Published: 06 December 2012

  • Series ISSN: 0930-0325

  • Series E-ISSN: 2197-7186

  • Edition Number: 1

  • Number of Pages: 164

  • Topics: Applications of Mathematics

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