Related papers: Learning interacting particle systems: diffusion p…
We study parameter estimation for interacting particle systems (IPSs) consisting of $N$ weakly interacting multivariate hypoelliptic SDEs. We propose a locally Gaussian approximation of the transition dynamics, carefully designed to address…
Diffusion of small particles is omnipresent in a plentiful number of processes occurring in Nature. As such, it is widely studied and exerted in almost all branches of sciences. It constitutes such a broad and often rather complex subject…
Considering the example of interacting Brownian particles we present a linear response derivation of the boundary condition for the corresponding hydrodynamic description (the diffusion equation). This requires us to identify a non-analytic…
Using the scheme of mesoscopic nonequilibrium thermodynamics, we construct the one- and two- particle Fokker-Planck equations for a system of interacting Brownian particles. By means of these equations we derive the corresponding balance…
We study the convergence of the empirical distribution associated with a system of interacting kinetic particles subject to independent Brownian forcing in a finite horizon setting, using some recent progress on kinetic non-linear partial…
In this paper, we consider nonlinear diffusion processes driven by space-time white noises, which have an interpretation in terms of partial differential equations. For a specific choice of coefficients, they correspond to the Landau…
In this paper we introduce a novel particle filter scheme for a class of partially-observed multivariate diffusions. %continuous-time dynamic models where the %signal is given by a multivariate diffusion process. We consider a variety of…
Modern developments in microscopy and image processing are revolutionising areas of physics, chemistry, and biology as nanoscale objects can be tracked with unprecedented accuracy. However, the price paid for having a direct visualisation…
The movement of a particle described by Brownian motion is quantified by a single parameter, $D$, the diffusion constant. The estimation of $D$ from a discrete sequence of noisy observations is a fundamental problem in biological single…
In this article we consider the estimation of static parameters for partially observed diffusion processes with discrete-time observations over a fixed time interval. In particular, when one only has access to time-discretized solutions of…
The diffusion coefficient--a measure of dissipation, and the entropy--a measure of fluctuation are found to be intimately correlated in many physical systems. Unlike the fluctuation dissipation theorem in linear response theory, the…
Experimental methods based on single particle tracking (SPT) are being increasingly employed in the physical and biological sciences, where nanoscale objects are visualized with high temporal and spatial resolution. SPT can probe…
We estimate the distribution of random parameters in a distributed parameter model with unbounded input and output for the transdermal transport of ethanol in humans. The model takes the form of a diffusion equation with the input being the…
We show that observing the trajectories of confined particles in a thermal equilibrium state yields an estimate on the free-space diffusion coefficient. For generic trapping potentials and interactions between particles, the estimate comes…
We consider a collection of weakly interacting diffusion processes moving in a two-scale locally periodic environment. We study the large deviations principle of the empirical distribution of the particles' positions in the combined limit…
We investigate a diffusive motion of a system of interacting Brownian particles in quasi-one-dimensional micropores. In particular, we consider a semi-infinite 1D geometry with a partially absorbing boundary and the hard-core inter-particle…
We study efficiency of non-parametric estimation of diffusions (stochastic differential equations driven by Brownian motion) from long stationary trajectories. First, we introduce estimators based on conditional expectation which is…
We use a deterministic particle method to produce numerical approximations to the solutions of an evolution cross-diffusion problem for two populations. According to the values of the diffusion parameters related to the intra and…
The well-posedness and regularity properties of diffusion-aggregation equations, emerging from interacting particle systems, are established on the whole space for bounded interaction force kernels by utilizing a compactness convergence…
For algorithms based on interacting particle systems that admit a mean-field description, convergence analysis is often more accessible at the mean-field level. In order to transfer convergence results obtained at the mean-field level to…