### Abstract

In this paper we propose an acceptance-rejection sampler using stratified inputs as driver sequence. We estimate the discrepancy of the N-point set in (s −s)-dimensions generated by this algorithm. First we show an upper bound on the star-discrepancy of order N
^{−d/2−1/(2s)}. Further we prove an upper bound on the qth moment of the L
_{q}-discrepancy (E[N
^{q} L
^{qq},N])
^{1/q} for 2 ≤ q ≤ ∞, which is of order N
^{(}
^{1−1/s)(1−1/q)}. The proposed approach is numerically tested and compared with the standard acceptance-rejection algorithm using pseudo-random inputs. We also present an improved convergence rate for a deterministic acceptance-rejection algorithm using (t, m, s)-nets as driver sequence.

Original language | English |
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Title of host publication | Monte Carlo and Quasi-Monte Carlo Methods |

Subtitle of host publication | MCQMC, Leuven, Belgium, April 2014 |

Editors | Ronald Cools, Dirk Nuyens |

Place of Publication | Cham |

Publisher | Springer, Springer Nature |

Pages | 599-619 |

Number of pages | 21 |

ISBN (Electronic) | 9783319335070 |

ISBN (Print) | 9783319335056 |

DOIs | |

Publication status | Published - 2016 |

Externally published | Yes |

Event | International Conference on Monte Carlo and Quasi-Monte Carlo Methods in Scientific Computing (11th : 2014) - KU Leuven, Belgium Duration: 6 Apr 2014 → 11 Apr 2014 |

### Publication series

Name | Springer Proceedings in Mathematics and Statistics |
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Publisher | Springer |

Volume | 163 |

ISSN (Print) | 2194-1009 |

ISSN (Electronic) | 2194-1017 |

### Conference

Conference | International Conference on Monte Carlo and Quasi-Monte Carlo Methods in Scientific Computing (11th : 2014) |
---|---|

Country | Belgium |

City | KU Leuven |

Period | 6/04/14 → 11/04/14 |

### Keywords

- Monte Carlo method
- Acceptance-rejection sampler
- Discrepancy theory

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## Cite this

*Monte Carlo and Quasi-Monte Carlo Methods: MCQMC, Leuven, Belgium, April 2014*(pp. 599-619). (Springer Proceedings in Mathematics and Statistics; Vol. 163). Cham: Springer, Springer Nature. https://doi.org/10.1007/978-3-319-33507-0_33