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On Generating Monte Carlo Samples of Continuous Diffusion Bridges

id: 2113 Date: 20131014 status: published Times:
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AuthorMing Lin, Rong Chen, Per Mykland
ContentDiffusion 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.
JEL-Codes
KeywordsStochastic diffusion equation, Sequential Monte Carlo, Resampling, Priority score, Backward pilot.
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