Simulation of Conditioned Diffusions on the Flat Torus
Research output: Chapter in Book/Report/Conference proceeding › Article in proceedings › Research › peer-review
Diffusion processes are fundamental in modelling stochastic dynamics in natural sciences. Recently, simulating such processes on complicated geometries has found applications for example in biology, where toroidal data arises naturally when studying the backbone of protein sequences, creating a demand for efficient sampling methods. In this paper, we propose a method for simulating diffusions on the flat torus, conditioned on hitting a terminal point after a fixed time, by considering a diffusion process in R2 which we project onto the torus. We contribute a convergence result for this diffusion process, translating into convergence of the projected process to the terminal point on the torus. We also show that under a suitable change of measure, the Euclidean diffusion is locally a Brownian motion.
Original language | English |
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Title of host publication | Geometric Science of Information - 4th International Conference, GSI 2019, Proceedings |
Editors | Frank Nielsen, Frédéric Barbaresco |
Number of pages | 10 |
Publisher | Springer VS |
Publication date | 2019 |
Pages | 685-694 |
ISBN (Print) | 9783030269791 |
DOIs | |
Publication status | Published - 2019 |
Event | 4th International Conference on Geometric Science of Information, GSI 2019 - Toulouse, France Duration: 27 Aug 2019 → 29 Aug 2019 |
Conference
Conference | 4th International Conference on Geometric Science of Information, GSI 2019 |
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Land | France |
By | Toulouse |
Periode | 27/08/2019 → 29/08/2019 |
Sponsor | École polytechnique, et al., Mines-ParisTech, SMAI, Sony Computer Science Laboratories Inc, Thales |
Series | Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) |
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Volume | 11712 LNCS |
ISSN | 0302-9743 |
- Conditioned diffusion, Flat Torus, Manifold diffusion, Simulation
Research areas
Links
- http://arxiv.org/pdf/1906.09813
Submitted manuscript
ID: 237711069