Many scientific fields have experienced growth in the use of stochastic differential equations
(SDEs), also known as diffusion processes, to model scientific phenomena over time. SDEs …

Rare event sampling in dynamical systems is a fundamental problem arising in the natural
sciences, which poses significant computational challenges due to an exponentially large …

We consider the problem of simulating diffusion bridges, which are diffusion processes that
are conditioned to initialize and terminate at two given states. The simulation of diffusion …

The article surveys and extends variational formulations of the thermodynamic free energy
and discusses their information-theoretic content from the perspective of mathematical …

A Monte Carlo method for simulating a multi-dimensional diffusion process conditioned on
hitting a fixed point at a fixed future time is developed. Proposals for such diffusion bridges …

Diffusion means in geometric spaces Page 1 Bernoulli 29(4), 2023, 3141–3170 https://doi.org/10.3150/22-BEJ1578
Diffusion means in geometric spaces BENJAMIN ELTZNER1,a, PERNILLE EH HANSEN2,b …

We consider estimation of scalar functions that determine the dynamics of diffusion
processes. It has been recently shown that nonparametric maximum likelihood estimation is …

Estimation of parameters of a diffusion based on discrete time observations poses a difficult
problem due to the lack of a closed form expression for the likelihood. From a Bayesian …

We develop a Bayesian inference method for diffusions observed discretely and with noise,
which is free of discretization bias. Unlike existing unbiased inference methods, our method …

With a view to statistical inference for discretely observed diffusion models, we propose
simple methods of simulating diffusion bridges, approximately and exactly. Diffusion bridge …