Conditional Path Sampling of SDEs and the Langevin MCMC Method

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details: , and : Conditional Path Sampling of SDEs and the Langevin MCMC Method. Communications in Mathematical Sciences, vol. 2, no. 4, pp. 685–697, 2004.
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keywords: MCMC methods, SPDEs, path sampling, Kalman filter
MSC2000: 65C05, 65C60, 60H15

Abstract

We introduce a stochastic PDE based approach to sampling paths of SDEs, conditional on observations. The SPDEs are derived by generalising the Langevin MCMC method to infinite dimensions. Various applications are described, including sampling paths subject to two end-point conditions (bridges) and nonlinear filter/smoothers.

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