Variance Reduction Techniques for the Simulation of Markov Processes. II. Matrix Iterative Methods.

Abstract

Let (x sub n, n > or = 0) be an irreducible, aperiodic, Markov chain with finite state space E, transition matrix P, and stationary distribution pi. Let f be a real valued function on E and define r = pi f. A method of reducing the variance of simulation estimates for r is presented. The method combines the techniques of numerical analysis and simulation by partially solving an appropriate system of linear equations using some matrix iterative procedure and then estimating the difference between the true and partial solutions via simulation. After k iterations of the iterative procedure, functions f sub nu, nu = 0, ..., k are defined so that r = pi f sub nu for each nu.

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Document Details

Document Type
Technical Report
Publication Date
Jan 01, 1978
Accession Number
ADA051430

Entities

People

  • Philip Heidelberger

Organizations

  • Stanford University

Tags

Communities of Interest

  • Materials and Manufacturing Processes

DTIC Thesaurus Topics

  • Differential Equations
  • Equations
  • Iterations
  • Markov Chains
  • Markov Processes
  • Military Research
  • Monte Carlo Method
  • Numerical Analysis
  • Operations Research
  • Partial Differential Equations
  • Probability
  • Probability Distributions
  • Random Variables
  • Simulations
  • Simulators
  • Stochastic Processes
  • Theorems

Fields of Study

  • Mathematics

Readers

  • Adaptive Control and Estimation with Uncertainty in Dynamic Systems.
  • Mathematical Modeling and Probability Theory.
  • Spectroscopy.

Technology Areas

  • Space