Guided Proposals for simulating multi-dimensional diffusion bridges
Artikel i vetenskaplig tidskrift, 2017

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.

Linear processes

Multidimensional diffusion bridge

Data augmentation

Change of measure

Författare

Moritz Schauer

Göteborgs universitet

Chalmers, Matematiska vetenskaper, Tillämpad matematik och statistik

Frank van der Meulen

TU Delft

Harry Van Zanten

Universiteit Van Amsterdam

Bernoulli

1350-7265 (ISSN)

Vol. 23 4A 2917-2950

Ämneskategorier (SSIF 2025)

Sannolikhetsteori och statistik

DOI

10.3150/16-BEJ833

Mer information

Senast uppdaterat

2025-07-01