Stable Processes and Related Topics: A Selection of Papers from the Mathematical Sciences Institute Workshop, January 9-13, 1990

ISBN-13: 9781468467802 / Angielski / Miękka / 2012 / 330 str.

Cambanis

Opis

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.

Spis treści

Gaussian measures of large balls in ?n.- On a Class of Infinitely Divisible Processes Represented as Mixtures of Gaussian Processes.- Capacities, Large Deviations and Loglog Laws.- Conditional variance of symmetric stable variables.- Bounded Stationary Stable Processes and Entropy.- Alternative multivariate stable distributions and their applications to financial modeling.- Construction of Multiple Stable Measures and Integrals Using LePage Representation.- Numerical computation of non-linear stable regression functions.- A Characterization of the Asymptotic Behavior of Stationary Stable Processes.- An Extremal Problem in Hp of the Upper Half Plane with Application to Prediction of Stochastic Processes.- On Multiple Markov S?S Processes.- On shot noise processes attracted to fractional Lévy motion.- Self-similar Stable Processes with Stationary Increments.- A Stochastic Integral Representation for the Bootstrap of the Sample Mean.- Multiple stable integrals appearing in weak limits.- Characterizations of ergodic stationary stable processes via the dynamical functional.