S. Liu, T. Kanamori, and D. J. Williams. Estimating density models with truncation boundaries using score matching. Journal of Machine Learning Research, 23(186):1-38, 2022. Cited on page 8.
Y. Liu. Discretization of a class of reflected diffusion processes. Mathematics and computers in simulation, 38(1-3):103-108, 1995. Cited on page 7.
Y. Liu. Numerical approaches to stochastic differential equations with boundary conditions. Purdue University, 1993. Cited on page 7.
A. Lou and S. Ermon. Reflected diffusion models. arXiv preprint arXiv:2304.04740, 2023. Cited on pages 2, 4, 5.
L. Lovász and S. Vempala. The geometry of logconcave functions and sampling algorithms. *Random Structures & Algorithms*, 30(3):307-358, 2007. Cited on page 7.
J. M. Lukens, K. J. Law, A. Jasra, and P. Lougovski. A practical and efficient approach for bayesian quantum state estimation. New Journal of Physics, 22(6):063038, 2020. Cited on page 1.
Met Office. Cartopy: a cartographic python library with a Matplotlib interface. Exeter, Devon, 2010 - 2015. URL: https://scitools.org.uk/cartopy. Cited on page 15.
B. J. Morris. Improved bounds for sampling contingency tables. *Random Structures & Algorithms*, 21(2):135-146, 2002. DOI: https://doi.org/10.1002/rsa.10049. eprint: https://onlinelibrary.wiley.com/doi/pdf/10.1002/rsa.10049. URL: https://onlinelibrary.wiley.com/doi/abs/10.1002/rsa.10049. Cited on page 1.
Natural Earth. Natural earth, 2023. URL: https://www.naturalearthdata.com/. [Online; accessed 31-Jan-2023]. Cited on page 15.
Y. Nesterov and A. Nemirovskii. Interior-point polynomial algorithms in convex programming. SIAM, 1994. Cited on page 4.
M. Noble, V. De Bortoli, and A. Durmus. Barrier Hamiltonian Monte Carlo, Oct. 2022. DOI: 10 . 48550/arXiv.2210.11925. Cited on page 2.
B. Pacchiarotti, C. Costantini, and F. Sartoretto. Numerical approximation for functionals of reflecting diffusion processes. SIAM Journal on Applied Mathematics, 58(1):73-102, 1998. Cited on page 7.
F. Petit. Time reversal and reflected diffusions. Stochastic Processes and their Applications, 69(1):25-53, July 1997. ISSN: 03044149. DOI: 10.1016/S0304-4149(97)00035-5. Cited on page 2.
R. Pettersson. Approximations for stochastic differential equations with reflecting convex boundaries. Stochastic processes and their applications, 59(2):295-308, 1995. Cited on page 7.
R. Pettersson. Penalization schemes for reflecting stochastic differential equations. Bernoulli:403-414, 1997. Cited on page 7.
A. Pilipenko. An introduction to stochastic differential equations with reflection, volume 1. Universitätsverlag Potsdam, 2014. Cited on page 7.
K. Ramanan. Reflected diffusions defined via the extended skorokhod map, 2006. Cited on pages 4, 14.
P. Rudiger, J. A. Bednar, J.-L. Stevens, M. Lique, C. B, S. H. Hansen, B. Little, Andrew, J. Signell, M. Hedley, C. Bosley, R. Hattersley, G. Brener, ea42gh, kbowen, A. Hilboll, I. Lustig, J. deWerd, N. Hand, R. Signell, J. Bampton, pmav99, scaine1, and zassa. Holoviz/geoviews: version 1.9.6, version v1.9.6, Jan. 2023. DOI: 10 .5281/zenodo .7543863. URL: https ://doi .org/10 . 5281/zenodo .7543863. Cited on page 16.
C. Saharia, W. Chan, S. Saxena, L. Li, J. Whang, E. L. Denton, K. Ghasemipour, R. Gontijo Lopes, B. Karagol Ayan, T. Salimans, et al. Photorealistic text-to-image diffusion models with deep language understanding. Advances in Neural Information Processing Systems, 35:36479-36494, 2022. Cited on page 2.
M. Shkolnikov and I. Karatzas. Time-reversal of reflected Brownian motions in the orthant, July 2013. URL: http://arxiv.org/abs/1307.4422. Cited on page 2.