  In this paper we develop a continuous-time sequential importance sampling
(CIS) algorithm which eliminates time-discretisation errors and provides online
unbiased estimation for continuous time Markov processes, in particular for
diffusions. Our work removes the strong conditions imposed by the EA and thus
extends significantly the class of discretisation error-free MC methods for
diffusions. The reason that CIS can be applied more generally than EA is that
it no longer works on the path space of the SDE. Instead it uses proposal
distributions for the transition density of the diffusion, and proposal
distributions that are absolutely continuous with respect to the true
transition density exist for general SDEs.
