On generating Monte Carlo samples of continuous diffusion bridges

Ming Lin, Rong Chen, Per Mykland

Research output: Contribution to journalArticlepeer-review

18 Scopus citations

Abstract

Diffusion processes are widely used in engineering, finance, physics, and other fields. Usually continuous-time diffusion processes can be observed only at discrete time points. For many applications, it is often useful to impute continuous-time bridge samples that follow the diffusion dynamics and connect each pair of the consecutive observations. The sequential Monte Carlo (SMC) method is a useful tool for generating the intermediate paths of the bridge. The paths often are generated forward from the starting observation and forced in some ways to connect with the end observation. In this article we propose a constrained SMC algorithm with an effective resampling scheme guided by backward pilots carrying the information of the end observation. This resampling scheme can be easily combined with any forward SMC sampler. Two synthetic examples are used to demonstrate the effectiveness of the resampling scheme.

Original languageEnglish (US)
Pages (from-to)820-838
Number of pages19
JournalJournal of the American Statistical Association
Volume105
Issue number490
DOIs
StatePublished - Jun 2010

All Science Journal Classification (ASJC) codes

  • Statistics and Probability
  • Statistics, Probability and Uncertainty

Keywords

  • Backward pilot
  • Priority score
  • Resampling
  • Sequential Monte Carlo
  • Stochastic diffusion equation

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