On the Functional Central Limit Theorem for Martingales

Abstract

Necessary and sufficient conditions for the functional central limit theorem for a double array of random variables are sought. It is argued that this is a martingale problem only if the variables truncated at some fixed point c are asymptotically a martingale difference array. Under this hypothesis, necessary and sufficient conditions for convergence in distribution to a Brownian motion are obtained when the normalization is given (i) by the sums of squares of the variables, (ii) by the conditional variances and (iii) by the variances. The results are proved by comparing the various normalizations with a 'natural' normalization.

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Document Details

Document Type
Technical Report
Publication Date
Nov 01, 1975
Accession Number
ADA018701

Entities

People

  • Holger Rootzen

Organizations

  • University of North Carolina at Chapel Hill

Tags

Communities of Interest

  • Materials and Manufacturing Processes

DTIC Thesaurus Topics

  • Brownian Motion
  • Classification
  • Contracts
  • Convergence
  • Mathematics
  • Military Research
  • North Carolina
  • Notation
  • Probability
  • Random Variables
  • Security
  • Statistics

Fields of Study

  • Mathematics

Readers

  • Mathematical Modeling and Probability Theory.
  • Structural Dynamics.