Guided proposals for simulating multi-dimensional diffusion bridges

Abstract

A Monte Carlo method for simulating a multi-dimensional diffusion process conditioned on hitting a fixed point at a fixed future time is developed. Proposals for such diffusion bridges are obtained by superimposing an additional guiding term to the drift of the process under consideration. The guiding term is derived via approximation of the target process by a simpler diffusion processes with known transition densities. Acceptance of a proposal can be determined by computing the likelihood ratio between the proposal and the target bridge, which is derived in closed form. We show under general conditions that the likelihood ratio is well defined and show that a class of proposals with guiding term obtained from linear approximations fall under these conditions.

References in corpus (4)

• Exact simulation of diffusions
• Simple simulation of diffusion bridges with application to likelihood inference for diffusions
• Bayesian estimation of discretely observed multi-dimensional diffusion processes using guided proposals
• Simulation of forward-reverse stochastic representations for conditional diffusions

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