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The study of sampling proposals for diffusion processes has been tackled numerous times in the literature. In practice, these are used to impute paths for a target diffusion process given a starting point and end-point, usually for inferential purposes. It would be preferable if sampling proposals remained stable also when observations are sparse. This paper discusses stability (or lack thereof) of proposal diffusions on classes of target diffusions as one increases the width of the interval, where the Kullback-Leibler divergence is used to measure similarity between two diffusion measures. Some stability-related results related to three proposals are proven. Two of the proposals we consider are the often-cited ones from Durham and Gallant, and Delyon and Hu.

Stability of sampling proposals for reducible diffusions over large time intervals