Optimal dependence on bridge endpoints

Determine the optimal dependence of exact multivariate diffusion bridge sampling work on the prescribed endpoints.

Background

For general bridge endpoints x and y, the paper's complexity bound depends on the quantity H_{T,x,y}=1+T+|y-x|2/T, but the minimax analysis does not establish whether this endpoint dependence is sharp. The authors explicitly state that optimal endpoint dependence remains unresolved.

References

The sharp joint dependence of bridge sampling work on the horizon and the number of requested observations remains open, as does the optimal dependence on the endpoints.

— Exact Simulation of Multivariate Diffusions and Bridges  (2610.11330 - Blanchet et al., 8 Oct 2026) in Section 4, Conclusions and discussions