Accession Number:

ADA275018

Title:

U-Statistics of Random-Size Samples and Limit Theorems for Systems of Markovian Particles with Non-Poisson Initial Distributions

Descriptive Note:

Corporate Author:

CALIFORNIA UNIV SANTA BARBARA

Personal Author(s):

Report Date:

1994-01-01

Pagination or Media Count:

21.0

Abstract:

Limiting distributions of square-integrable infinite order U- statistics were first studied by Dynkin and Mandelbaum 1983 and Mandelbaum and Taqqu 1984. We extend their results to the case of non-Poisson random sample size. Multiple integrals of non-Gaussian generalized fields are constructed to identify the limiting distributions. An invariance principle is also established. We use these results to study the limiting distribution of the amount of charge left in some set by an infinite system of signed Markovian particles when the initial particle density goes to infinity. By selecting the initial particle distribution, we determine the limiting distribution of charge, constructing different non-Gaussian generalized random fields, including Laplace, alpha-stable, and their multiple integrals.

Subject Categories:

  • Statistics and Probability

Distribution Statement:

APPROVED FOR PUBLIC RELEASE