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Stable Processes and Related Topics

A Selection of Papers from the Mathematical Sciences Institute Workshop, January 9–13, 1990

  • Book
  • © 1991

Overview

Editors:
  1. Stamatis Cambanis

    1. Department of Statistics, University of North Carolina, Chapel Hill, USA

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  2. Gennady Samorodnitsky

    1. Engineering Theory Center, Cornell University, Ithaca, USA

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    You can also search for this editor in PubMed   Google Scholar

  3. Murad S. Taqqu

    1. Department of Mathematics, Boston University, Boston, USA

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    You can also search for this editor in PubMed   Google Scholar

Part of the book series: Progress in Probability (PRPR, volume 25)

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Table of contents (16 chapters)

  1. Front Matter

    Pages I-IX
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  2. Gaussian measures of large balls in ℝn

    • Werner Linde
    Pages 1-25

  3. On A Class of Infinitely Divisible Processes Represented as Mixtures of Gaussian Processes

    • Jan Rosinski
    Pages 27-41

  4. Capacities, Large Deviations and Loglog Laws

    • George L. O’brien, Wim Vervaat
    Pages 43-83

  5. Conditional variance of symmetric stable variables

    • Wei Wu, Stamatis Cambanis
    Pages 85-99

  6. Bounded Stationary Stable Processes and Entropy

    • John P. Nolan
    Pages 101-105

  7. Alternative multivariate stable distributions and their applications to financial modeling

    • Stefan Mittnik, Svetlozar T. Rachev
    Pages 107-119

  8. Construction of Multiple Stable Measures and Integrals Using Lepage Representation

    • Gennady Samorodnitsky, Murad S. Taqqu
    Pages 121-141

  9. Numerical computation of non-linear stable regression functions

    • Clyde D. Hardin Jr., Gennady Samorodnitsky, Murad S. Taqqu
    Pages 143-180

  10. A Characterization of the Asymptotic Behavior of Stationary Stable Processes

    • Joshua B. Levy, Murad S. Taqqu
    Pages 181-198

  11. An Extremal Problem in Hp of the Upper Half Plane with Application to Prediction of Stochastic Processes

    • Balram S. Rajput, Kavi Rama-Murthy, Carl Sundberg
    Pages 199-252

  12. On Multiple Markov SαS Processes

    • V. Mandrekar, B. Thelen
    Pages 253-260

  13. On shot noise processes attracted to fractional Lévy motion

    • L. Giraitis, D. Surgailis
    Pages 261-273

  14. Self-Similar Stable Processes with Stationary Increments

    • Norio Kôno, Makoto Maejima
    Pages 275-295

  15. A Stochastic Integral Representation for the Bootstrap of the Sample Mean

    • John Kinateder
    Pages 297-303

  16. Multiple stable integrals appearing in weak limits

    • Jerzy Szulga
    Pages 305-316

  17. Characterizations of ergodic stationary stable processes via the dynamical functional

    • Krzysztof Podgórski, Aleksander Weron
    Pages 317-328

  18. Back Matter

    Pages 329-329
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Keywords

About this book

The Workshop on Stable Processes and Related Topics took place at Cor­ nell University in January 9-13, 1990, under the sponsorship of the Mathemat­ ical Sciences Institute. It attracted an international roster of probabilists from Brazil, Japan, Korea, Poland, Germany, Holland and France as well as the U. S. This volume contains a sample of the papers presented at the Workshop. All the papers have been refereed. Gaussian processes have been studied extensively over the last fifty years and form the bedrock of stochastic modeling. Their importance stems from the Central Limit Theorem. They share a number of special properties which facilitates their analysis and makes them particularly suitable to statistical inference. The many properties they share, however, is also the seed of their limitations. What happens in the real world away from the ideal Gaussian model? The non-Gaussian world may contain random processes that are close to the Gaussian. What are appropriate classes of nearly Gaussian models and how typical or robust is the Gaussian model amongst them? Moving further away from normality, what are appropriate non-Gaussian models that are sufficiently different to encompass distinct behavior, yet sufficiently simple to be amenable to efficient statistical inference? The very Central Limit Theorem which provides the fundamental justifi­ cation for approximate normality, points to stable and other infinitely divisible models. Some of these may be close to and others very different from Gaussian models.

Editors and Affiliations

  • Department of Statistics, University of North Carolina, Chapel Hill, USA

    Stamatis Cambanis

  • Engineering Theory Center, Cornell University, Ithaca, USA

    Gennady Samorodnitsky

  • Department of Mathematics, Boston University, Boston, USA

    Murad S. Taqqu

Bibliographic Information

  • Book Title: Stable Processes and Related Topics

  • Book Subtitle: A Selection of Papers from the Mathematical Sciences Institute Workshop, January 9–13, 1990

  • Editors: Stamatis Cambanis, Gennady Samorodnitsky, Murad S. Taqqu

  • Series Title: Progress in Probability

  • DOI: https://doi.org/10.1007/978-1-4684-6778-9

  • Publisher: Birkhäuser Boston, MA

  • eBook Packages: Springer Book Archive

  • Copyright Information: Birkhäuser Boston 1991

  • Softcover ISBN: 978-1-4684-6780-2Published: 14 March 2012

  • eBook ISBN: 978-1-4684-6778-9Published: 06 December 2012

  • Series ISSN: 1050-6977

  • Series E-ISSN: 2297-0428

  • Edition Number: 1

  • Number of Pages: X, 330

  • Topics: Probability Theory and Stochastic Processes

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