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A system of diffusion-reaction equations coupled with a dissolution-precipitation model is discussed. We start by introducing a microscale model together with its homogenized version. In the present paper, we first derive the corrector…
In this paper we consider the filtering of partially observed multi-dimensional diffusion processes that are observed regularly at discrete times. We assume that, for numerical reasons, one has to time-discretize the diffusion process which…
We propose a new semiparametric approach for modelling nonlinear univariate diffusions, where the observed process is a nonparametric transformation of an underlying parametric diffusion (UPD). This modelling strategy yields a general class…
The diffusion coefficient of a circular shaped inclusion in a liquid membrane is investigated by taking into account the interaction between membranes and bulk solvents of arbitrary thickness. As illustrative examples, the diffusion…
This paper concerns the use of the expectation-maximisation (EM) algorithm for inference in partially observed diffusion processes. In this context, a well known problem is that all except a few diffusion processes lack closed-form…
Variable selection for high-dimensional, highly correlated data has long been a challenging problem, often yielding unstable and unreliable models. We propose a resample-aggregate framework that exploits diffusion models' ability to…
We consider the problem of statistical inference for the effective dynamics of multiscale diffusion processes with (at least) two widely separated characteristic time scales. More precisely, we seek to determine parameters in the effective…
Probabilistic regression models the entire predictive distribution of a response variable, offering richer insights than classical point estimates and directly allowing for uncertainty quantification. While diffusion-based generative models…
In many important statistical applications, the number of variables or parameters $p$ is much larger than the number of observations $n$. Suppose then that we have observations $y=X\beta+z$, where $\beta\in\mathbf{R}^p$ is a parameter…
A general theory of efficient estimation for ergodic diffusion processes sampled at high frequency with an infinite time horizon is presented. High frequency sampling is common in many applications, with finance as a prominent example. The…
The Langevin equation is a common tool to model diffusion at a single-particle level. In non-homogeneous environments, such as aqueous two-phase systems or biological condensates with different diffusion coefficients in different phases,…
The problem of diffusion in a porous medium with a spatially varying porosity is considered. The particular microstructure analyzed comprises a collection of impenetrable spheres, though the methods developed are general. Two different…
In this paper we investigate deterministic diffusion in systems which are spatially extended in certain directions but are restricted in size and open in other directions, consequently particles can escape. We introduce besides the…
This paper deals with the problem of density estimation. We aim at building an estimate of an unknown density as a linear combination of functions of a dictionary. Inspired by Cand\`es and Tao's approach, we propose an $\ell_1$-minimization…
We treat the change point problem in ergodic diffusion processes from discrete observations. Tonaki et al. (2020) proposed adaptive tests for detecting changes in the diffusion and drift parameters in ergodic diffusion models. When any…
We consider a simple mean reverting diffusion process, with piecewise constant drift and diffusion coefficients, discontinuous at a fixed threshold. We discuss estimation of drift and diffusion parameters from discrete observations of the…
We develop diffusion-based samplers for target distributions known up to a normalising constant. To this end, we rely on the well-known diffusion path that smoothly interpolates between a simple base distribution and the target, popularised…
Improving the efficiency of discrete time scale invariant (DSI) processes, we consider some flexible sampling of a continuous time DSI process ${X(t), t\in{R^+}}$ with scale $l>1$, which is in correspondence to some multi-dimensional…
Translational diffusion coefficients are routinely estimated from molecular dynamics simulations. Linear fits to mean squared displacement (MSD) curves have become the de facto standard, from simple liquids to complex biomacromolecules.…
The behavior of slow-fast diffusions as the separation of scale diverges is a well-studied problem in the literature. In this short paper, we revisit this problem and obtain a new proof of existing strong quantitative convergence estimates…