Trapezoidal Stratified Monte Carlo Integration

Abstract

Weighted integrals of random processes are approximated by the trapezoidal rule based on a stratified and symmetrized random sample of size n. The weight functions are assumed to be twice continuously differentiable. We consider the rate of convergence to zero of the mean-square integral approximation error as the sample size increases indefinitely. For random processes which are twice mean-square continuously differentiable it is shown that the rate is N to the minus 5th power, just as without a random component. For random processes which are a bit more than once, but not twice, mean-square continuously differentiable the rate is shown to be N to the minus 4th power. In both cases the asymptotic constant is also determined. (KR)

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Document Details

Document Type
Technical Report
Publication Date
Mar 01, 1990
Accession Number
ADA223565

Entities

People

  • Elias Masry

Organizations

  • University of North Carolina at Chapel Hill

Tags

DTIC Thesaurus Topics

  • Air Force
  • Convergence
  • Covariance
  • Data Science
  • Information Science
  • Integrals
  • Monte Carlo Method
  • North Carolina
  • Probability
  • Random Variables
  • Stationary Processes
  • Statistical Algorithms
  • Statistical Analysis
  • Statistical Samples
  • Statistics
  • Stochastic Processes
  • Theorems

Fields of Study

  • Mathematics

Readers

  • Calculus or Mathematical Analysis
  • Statistical inference.