WEAK CONVERGENCE OF PROBABILITY MEASURES ON PRODUCT SPACES WITH APPLICATIONS TO SUMS OF RANDOM VECTORS,

Abstract

Let C superscript k be the product of k copies of C(0,1), the space of continuous functions on (0,1) with the uniform metric, and D superscript k the product of k copies of D(0,1), the space of right continuous functions on (0,1) having left limits with the Skorohod metric. Necessary and sufficient conditions are obtained for the weak convergence of a sequence of probability measures (Pn) on C superscript k (or D superscript k) to a probability measure P. These results are then applied to obtain functional central limit theorems for sums of random vectors. The random vectors considered are either independent and identically distributed or stationary phi-mixing. Extensions to the case of sums of a random number of random variables are also treated. (Author)

Document Details

Document Type
Technical Report
Publication Date
Mar 04, 1968
Accession Number
AD0666557

Entities

People

  • Donald Iglehart

Organizations

  • Stanford University

Tags

DTIC Thesaurus Topics

  • Contracts
  • Convergence
  • Cooperation
  • Mathematics
  • Probability
  • Probability Distributions
  • Random Variables
  • Sequences
  • Stationary
  • Stochastic Processes
  • Weak Convergence

Fields of Study

  • Mathematics

Readers

  • Mathematical Modeling and Probability Theory.

Technology Areas

  • Space