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

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.

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Document Details

Document Type
Technical Report
Publication Date
Jan 01, 1994
Accession Number
ADA275018

Entities

People

  • Raisa E. Feldman
  • Svetlozar Rachev

Organizations

  • University of California, Santa Barbara

Tags

Communities of Interest

  • Materials and Manufacturing Processes

DTIC Thesaurus Topics

  • Convergence
  • Data Science
  • Gaussian Distributions
  • Gaussian Processes
  • Information Science
  • Integrals
  • Invariance
  • Markov Processes
  • New York
  • Probability
  • Random Variables
  • Sequences
  • Statistics
  • Stochastic Processes
  • Surveys
  • Theorems
  • Weak Convergence

Fields of Study

  • Mathematics

Readers

  • Aerosol Science/Aerosol Physics
  • Mathematical Modeling and Probability Theory.
  • Statistical inference.