Strong Representation of Weak Convergence.

Abstract

This result is proved. If sub n is a separable metric space for n<or = infinity, phi sub n: S sub n approaches limit of S sub infinity is measurable for < sub infinity, X sub n is an S sub n valued random variable for n<or = infinity and phi sub n (X sub n) approaches limit of sub x sub infinity in S sub infinity, then there exists S sub n valued random variables X sub n such that X sub n = d sub x sub n for n<or = infinity and phi sub n (X sub n) approaches limit of X sub infinity wpl. Conditions on S sub n and phi sub n are presented that allow a construction in the context of Polish spaces.

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Document Details

Document Type
Technical Report
Publication Date
Jun 01, 1987
Accession Number
ADA186433

Entities

People

  • W. Q. Liang
  • W. Vervaat
  • Z. D. Bai

Organizations

  • University of North Carolina at Chapel Hill

Tags

Communities of Interest

  • Materials and Manufacturing Processes

DTIC Thesaurus Topics

  • Acquisition
  • Availability
  • Classification
  • Construction
  • Convergence
  • North Carolina
  • Probability
  • Random Variables
  • Security
  • Statistics
  • Stochastic Processes
  • Weak Convergence

Readers

  • Analytical Mechanics
  • Mathematical Modeling and Probability Theory.

Technology Areas

  • Space
  • Space - Spacecraft Maneuvers