Guided proposals for simulating multi-dimensional diffusion bridges (Q2405130)

The problem of Monte Carlo simulation of a multidimensional diffusion bridge, i.e., a diffusion conditioned to be at a specific point at a specific time in future, is considered. The actual conditional law involves the unknown density, so is unavailable for forming the proposal distribution. In view of this, a scheme is developed in order to derive a proposal distribution, in terms of an auxiliary diffusion, that can be shown to be absolutely continuous with respect to the target distribution under a set of assumptions. These assumptions are shown to hold for a class of linear diffusions. Numerical evidence in support of the proposed scheme is presented.