Papers › Simulating conditioned diffusions on manifolds
Simulating conditioned diffusions on manifolds
Marc Corstanje, Frank van der Meulen, Moritz Schauer, Stefan Sommer
The archive published only this paper's code-link row. Authors, date and abstract are from arXiv's metadata (CC0), read from the Kaggle arXiv metadata snapshot of 2026-09-12 where its title matched the archive's; the title is the archive's.
To date, most methods for simulating conditioned diffusions are limited to the Euclidean setting. The conditioned process can be constructed using a change of measure known as Doob's h-transform. The specific type of conditioning depends on a function h which is typically unknown in closed form. To resolve this, we extend the notion of guided processes to a manifold M, where one replaces h by a function based on the heat kernel on M. We consider the case of a Brownian motion with drift, constructed using the frame bundle of M, conditioned to hit a point x_T at time T. We prove equivalence of the laws of the conditioned process and the guided process with a tractable Radon-Nikodym derivative. Subsequently, we show how one can obtain guided processes on any manifold N that is diffeomorphic to M without assuming knowledge of the heat kernel on N. We illustrate our results with numerical simulations of guided processes and Bayesian parameter estimation based on discrete-time observations. For this, we consider both the torus and the Poincar\'e disk.
Code
Repository list and official/mentioned flags are the archive's, frozen 2025-07-28. Reachability, where shown, is from one Syntology probe window (2026-09-16 to 2026-09-18); repositories not probed show nothing. GitHub stars are not tracked.
Code Syntology ran Syntology
Not run by Syntology. Nothing on this page verifies that the listed code works.
Results from the paper archive 2025-07-28
No leaderboard rows for this paper in the archive.
Report a problem or propose a change · a person checks every report against the paper or source before anything changes; decisions are listed on /corrections