Simulation of Conditioned Diffusions on the Flat Torus

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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 languageEnglish
Title of host publicationGeometric Science of Information - 4th International Conference, GSI 2019, Proceedings
EditorsFrank Nielsen, Frédéric Barbaresco
Number of pages10
PublisherSpringer VS
Publication date2019
ISBN (Print)9783030269791
Publication statusPublished - 2019
Event4th International Conference on Geometric Science of Information, GSI 2019 - Toulouse, France
Duration: 27 Aug 201929 Aug 2019


Conference4th International Conference on Geometric Science of Information, GSI 2019
SponsorÉcole polytechnique, et al., Mines-ParisTech, SMAI, Sony Computer Science Laboratories Inc, Thales
SeriesLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume11712 LNCS

    Research areas

  • Conditioned diffusion, Flat Torus, Manifold diffusion, Simulation


ID: 237711069