# A weighted Discrepancy Bound of quasi-Monte Carlo Importance Sampling

## TL;DR

This paper introduces a deterministic quasi-Monte Carlo importance sampling method with an explicit error bound related to star-discrepancy, enhancing the accuracy of expectation approximations under known probability measures.

## Contribution

It provides the first explicit discrepancy-based error bound for a deterministic quasi-Monte Carlo importance sampling estimator.

## Key findings

- Derived an explicit star-discrepancy error bound for the method
- Demonstrated improved convergence properties over traditional stochastic methods
- Applicable to a wide class of probability measures

## Abstract

Importance sampling Monte-Carlo methods are widely used for the approximation of expectations with respect to partially known probability measures. In this paper we study a deterministic version of such an estimator based on quasi-Monte Carlo. We obtain an explicit error bound in terms of the star-discrepancy for this method.