On Generating Monte Carlo Samples of Continuous Diffusion Bridges
Ming Lin, Rong Chen, Per Mykland
Journal of the American Statistical Association
#002113 20131014 (published)
Diffusion processes are widely used in engineering, fiance, physics and other fields. Usually continuous time diffusion processes are only observable 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 to generate the intermediate paths of the bridge. Often the paths are generated forward from the starting observation and forced in some ways to connect with the end observation. In this paper we propose a constrained SMC algorithm with an effective resampling scheme that is 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.
Keywords: Stochastic diffusion equation, Sequential Monte Carlo, Resampling, Priority score, Backward pilot.

Download full text