Related papers: Learning interacting particle systems: diffusion p…
In this paper we obtain uniform propagation estimates for systems of interacting diffusions. We adopt a general model, satisfying various conditions which ensure that the decay resulting from the internal dynamics term dominates the…
We consider a system of $N$ interacting particles, governed by transport and diffusion, that converges in a mean-field limit to the solution of a McKean-Vlasov equation. From the observation of a trajectory of the system over a fixed time…
In this paper we study macroscopic density equations in which the diffusion coefficient depends on a weighted spatial average of the density itself. We show that large differences (not present in the local density-dependence case) appear…
A finite dimensional abstract approximation and convergence theory is developed for estimation of the distribution of random parameters in infinite dimensional discrete time linear systems with dynamics described by regularly dissipative…
Particle filtering is a Bayesian inference method and a fundamental tool in state estimation for dynamic systems, but its effectiveness is often limited by the constraints of the initial prior distribution, a phenomenon we define as the…
The present paper discusses the diffusion approximation of the linear Boltzmann equation in cases where the collision frequency is not uniformly large in the spatial domain. Our results apply for instance to the case of radiative transfer…
Modern developments in microscopy and image processing are revolutionizing areas of physics, chemistry and biology as nanoscale objects can be tracked with unprecedented accuracy. The goal of single particle tracking is to determine the…
We present a Bayesian methodology for infinite as well as finite dimensional parameter identification for partial differential equation models. The Bayesian framework provides a rigorous mathematical framework for incorporating prior…
We address the issue of the proximity of interacting diffusion models on large graphs with a uniform degree property and a corresponding mean field model, i.e. a model on the complete graph with a suitably renormalized interaction…
We present an efficient point-particle approach to simulate reaction-diffusion processes of spherical absorbing particles in the diffusion-limited regime, as simple models of cellular uptake. The exact solution for a single absorber is used…
Although driven Brownian particles are ubiquitous in stochastic dynamics and often serve as paradigmatic model systems for many aspects of stochastic thermodynamics, fully analytically solvable models are few and far between. In this paper,…
Brownian Dynamics algorithms are widely used for simulating soft-matter and biochemical systems. In recent times, their application has been extended to the simulation of coarse-grained models of cellular networks in simple organisms. In…
We calculate the diffusion coefficient of an active tracer in a schematic crowded environment, represented as a lattice gas of passive particles with hardcore interactions. Starting from the master equation of the problem, we put forward a…
The aim of this review is to provide a concise overview of some of the generic approaches that have been developed to deal with the statistical description of large systems of interacting dissipative 'units'. The latter notion includes,…
In this paper, we study the problem of parameter estimation in a sensor network, where the measurements and updates of some sensors might be arbitrarily manipulated by adversaries. Despite the presence of such misbehaviors, normally…
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 develop and implement new probabilistic strategy for proving basic results about long time behaviour for interacting diffusion processes on unbounded lattice. The concept of the solution used is rather weak as we construct the process as…
We discuss parametric estimation of a degenerate diffusion system from time-discrete observations. The first component of the degenerate diffusion system has a parameter $\theta_1$ in a non-degenerate diffusion coefficient and a parameter…
We consider the problem of parameter estimation in the case of observation of the trajectory of diffusion process. We suppose that the drift coefficient has a singularity of cusp-type and the unknown parameter corresponds to the position of…
In this paper we provide a physical interpretation of It\^o-process resulting in thermal equilibrium distribution of a Brownian particle experiencing coordinate dependent diffusion. Since the local quantities like diffusivity would go…