## Abstract

In this article, we consider the multilevel sequential Monte Carlo (MLSMC) method of Beskos et al. (Stoch. Proc. Appl. [to appear]). This is a technique designed to approximate expectations w.r.t. probability laws associated to a discretization. For instance, in the context of inverse problems, where one discretizes the solution of a partial differential equation. The MLSMC approach is especially useful when independent, coupled sampling is not possible. Beskos et al. show that for MLSMC the computational effort to achieve a given error, can be less than independent sampling. In this article we significantly weaken the assumptions of Beskos et al., extending the proofs to non-compact state-spaces. The assumptions are based upon multiplicative drift conditions as in Kontoyiannis and Meyn (Electron. J. Probab. 10 [2005]: 61–123). The assumptions are verified for an example.

Original language | English |
---|---|

Pages (from-to) | 478-498 |

Number of pages | 21 |

Journal | Stochastic Analysis and Applications |

Volume | 35 |

Issue number | 3 |

Early online date | 9 Jan 2017 |

DOIs | |

Publication status | Published - 2017 |

## Keywords

- drift conditions
- Multilevel Monte Carlo
- sequential Monte Carlo