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

We consider the multilevel sequential Monte Carlo (MLSMC) method of Beskos et al. (Stoch. Proc. Appl. [to appear]). This technique is 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.
Authors:
 [1] ;  [2] ;  [3]
  1. Univ. of Bordeaux (France)
  2. National Univ. of Singapore (Singapore)
  3. Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States)
Publication Date:
Grant/Contract Number:
AC05-00OR22725
Type:
Accepted Manuscript
Journal Name:
Stochastic Analysis and Applications
Additional Journal Information:
Journal Volume: 35; Journal Issue: 3; Journal ID: ISSN 0736-2994
Research Org:
Oak Ridge National Laboratory (ORNL), Oak Ridge, TN (United States). Center for Nanophase Materials Sciences (CNMS)
Sponsoring Org:
USDOE
Country of Publication:
United States
Language:
English
Subject:
97 MATHEMATICS AND COMPUTING
OSTI Identifier:
1361332