Nearby Variables with Nearby Conditional Laws and a Strong Approximation Theorem for Hilbert Space Valued Martingales

Abstract

This paper focuses on sequences of random vectors which do not admit a strong approximation of their partial sums by sums of independent random vectors. The first part proves conditional versions of the Strassen-Dudley theorem. These are applied to obtain strong invariance principles for vector- valued martingales which, when properly normalized, converge in law to a mixture of Gaussian distributions. Keywords: Mathematical models, Random variables.

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Document Details

Document Type
Technical Report
Publication Date
Apr 01, 1989
Accession Number
ADA225992

Entities

People

  • D. Monrad
  • W. Philipp

Organizations

  • University of North Carolina at Chapel Hill

Tags

Communities of Interest

  • Materials and Manufacturing Processes

DTIC Thesaurus Topics

  • Air Force
  • Brownian Motion
  • Data Science
  • Differential Equations
  • Equations
  • Gaussian Distributions
  • Gaussian Processes
  • Hilbert Space
  • Information Science
  • North Carolina
  • Probability
  • Random Variables
  • Sequences
  • Statistics
  • Stochastic Processes
  • Two Dimensional
  • Universities

Fields of Study

  • Mathematics

Readers

  • Mathematical Modeling and Probability Theory.

Technology Areas

  • Space