TY - JOUR

T1 - Multilevel sequential Monte Carlo: Mean square error bounds under verifiable conditions

AU - Del Moral, Pierre

AU - Jasra, Ajay

AU - Law, Kody J.H.

N1 - Generated from Scopus record by KAUST IRTS on 2019-11-20

PY - 2017/5/4

Y1 - 2017/5/4

N2 - 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.

AB - 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.

UR - https://www.tandfonline.com/doi/full/10.1080/07362994.2016.1272421

UR - http://www.scopus.com/inward/record.url?scp=85008678043&partnerID=8YFLogxK

U2 - 10.1080/07362994.2016.1272421

DO - 10.1080/07362994.2016.1272421

M3 - Article

SN - 1532-9356

VL - 35

JO - Stochastic Analysis and Applications

JF - Stochastic Analysis and Applications

IS - 3

ER -