Subsolutions of an Isaacs Equation and Efficient Schemes for Importance Sampling: Convergence Analysis

Abstract

Previous papers by authors establish the connection between importance sampling algorithms for estimating rare-event probabilities, two-person zero-sum differential games, and the associated Isaacs equation. In order to construct nearly optimal schemes in a general setting, one must consider dynamic schemes, i.e., changes of measure that, in the course of a single simulation, can depend on the outcome of the simulation up till that time. The present paper and a companion paper show that classical sense subsolutions of the Isaacs equation provide a basic and flexible tool for the construction and analysis of nearly optimal schemes. Asymptotic analysis is the topic of the present paper, while the companion paper focuses on explicit methods for the construction of subsolutions, implementation aspects and numerical results.

Open PDF

Document Details

Document Type
Technical Report
Publication Date
Aug 08, 2005
Accession Number
ADA458989

Entities

People

  • Hui Wang
  • Paul Dupuis

Organizations

  • Brown University

Tags

Communities of Interest

  • Materials and Manufacturing Processes

DTIC Thesaurus Topics

  • Applied Mathematics
  • Construction
  • Convergence
  • Differential Equations
  • Eigenvectors
  • Equations
  • Inequalities
  • Markov Chains
  • Markov Processes
  • Mathematics
  • Partial Differential Equations
  • Probability
  • Random Variables
  • Sampling
  • Stochastic Control
  • Stochastic Processes
  • Weak Convergence

Fields of Study

  • Mathematics

Readers

  • Game Theory.
  • Linear Algebra
  • Systems Analysis and Design