Continuous-discrete smoothing of diffusions

摘要: Suppose X is a multivariate diffusion process that observed discretely in time. At each observation time, linear transformation of the state with noise. The smoothing problem consists recovering path process, consistent observations. We derive novel Markov Chain Monte Carlo algorithm to sample from exact distribution. resulting called Backward Filtering Forward Guiding (BFFG) algorithm. extend include parameter estimation. proposed method relies on guided proposals introduced Schauer et al. (2017). illustrate its efficiency number challenging problems.