Exact Simulation of Multivariate Diffusions and Bridges
Abstract
We provide the first generic exact sampling algorithms with finite expected total cost for uniformly elliptic multivariate diffusions and the corresponding diffusion bridges with bounded coefficients and bounded continuous first derivatives. We formulate a computational cost model that counts work in terms of generation of Gaussian and uniform random variables to execute acceptance--rejection sampling, as well as function evaluations of the drift and diffusion coefficients, together with elementary operations such as sums and multiplications. Our constructions combine randomized parametrix expansions with a finite weighted graph that incorporates both bridge endpoints into the proposal. The exact sampling of the diffusion is minimax optimal jointly in the horizon and number of requested observations, while bridge sampling is minimax optimal in the number of observations for fixed horizon and endpoints.
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BibTeX
@misc{blanchet2026exact,
title = {{Exact Simulation of Multivariate Diffusions and Bridges}},
author = {Jose Blanchet and Jikai Jin and Hao Liu},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.11330},
eprint = {2610.11330},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.11330},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Exact Simulation of Multivariate Diffusions and Bridges
AU - Jose Blanchet
AU - Jikai Jin
AU - Hao Liu
PY - 2026
DA - 2026/10/08
PB - arXiv
DO - 10.48550/arxiv.2610.11330
UR - https://arxiv.org/abs/2610.11330
AB - We provide the first generic exact sampling algorithms with finite expected total cost for uniformly elliptic multivariate diffusions and the corresponding diffusion bridges with bounded coefficients and bounded continuous first derivatives. We formulate a computational cost model that counts work in terms of generation of Gaussian and uniform random variables to execute acceptance--rejection sampling, as well as function evaluations of the drift and diffusion coefficients, together with elementary operations such as sums and multiplications. Our constructions combine randomized parametrix expansions with a finite weighted graph that incorporates both bridge endpoints into the proposal. The exact sampling of the diffusion is minimax optimal jointly in the horizon and number of requested observations, while bridge sampling is minimax optimal in the number of observations for fixed horizon and endpoints.
ER -