On Unbiased Estimation for Partially Observed Diffusions

We consider a class of diffusion processes with finite-dimensional parameters and partially observed at discrete time instances. We propose a methodology to unbiasedly estimate the expectation of a given functional of the diffusion process conditional on parameters and data. When these unbiased estimators with appropriately chosen functionals are employed within an expectation-maximization algorithm or a stochastic gradient method, this enables statistical inference using the maximum likelihood or Bayesian framework. Compared to existing approaches, the use of our unbiased estimators allows …

algorithm class data diffusion expectation-maximization functional instances methodology parameters process processes unbiased