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Stable Processes and Related Topics

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

  • Stamatis Cambanis
  • Gennady Samorodnitsky
  • Murad S. Taqqu

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

Table of contents

  1. Front Matter
    Pages I-IX
  2. George L. O’brien, Wim Vervaat
    Pages 43-83
  3. Wei Wu, Stamatis Cambanis
    Pages 85-99
  4. Clyde D. Hardin Jr., Gennady Samorodnitsky, Murad S. Taqqu
    Pages 143-180
  5. V. Mandrekar, B. Thelen
    Pages 253-260
  6. L. Giraitis, D. Surgailis
    Pages 261-273
  7. Norio Kôno, Makoto Maejima
    Pages 275-295
  8. Back Matter
    Pages 329-329

About this book

Introduction

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.

Keywords

Finite Gaussian measure Gaussian process Statistica Variance Volume behavior boundary element method form random processes statistical inference stochastic process stochastic processes theorem university

Editors and affiliations

  • Stamatis Cambanis
    • 1
  • Gennady Samorodnitsky
    • 2
  • Murad S. Taqqu
    • 3
  1. 1.Department of StatisticsUniversity of North CarolinaChapel HillUSA
  2. 2.Engineering Theory CenterCornell UniversityIthacaUSA
  3. 3.Department of MathematicsBoston UniversityBostonUSA

Bibliographic information