Related papers: Learning interacting particle systems: diffusion p…
In this paper we study the diffusion approximation of a swarming model given by a system of interacting Langevin equations with nonlinear friction. The diffusion approximation requires the calculation of the drift and diffusion coefficients…
A parameter estimation problem is considered for a stochastic parabolic equation with multiplicative noise under the assumption that the equation can be reduced to an infinite system of uncoupled diffusion processes. From the point of view…
We study the joint asymptotic behavior of spacings between particles at the edge of multilevel Dyson Brownian motions, when the number of levels tends to infinity. Despite the global interactions between particles in multilevel Dyson…
Estimating parameters of a diffusion process given continuous-time observations of the process via maximum likelihood approaches or, online, via stochastic gradient descent or Kalman filter formulations constitutes a well-established…
We examine the behavior of $n$ Brownian particles diffusing on the real line with bounded, measurable drift and bounded, piecewise continuous diffusion coefficients that depend on the current configuration of particles. Sufficient…
For a class of interacting particle systems in continuous space, we show that finite-volume approximations of the bulk diffusion matrix converge at an algebraic rate. The models we consider are reversible with respect to the Poisson…
We study heterogeneously interacting diffusive particle systems with mean-field type interaction characterized by an underlying graphon and their finite particle approximations. Under suitable conditions, we obtain exponential concentration…
In this paper, we investigate gradient estimate of the Poisson equation and the exponential convergence in the Wasserstein metric $W_{1,d_{l^1}}$, uniform in the number of particles, and uniform-in-time propagation of chaos for the…
We consider a class of interacting particle systems in continuous space of non-gradient type, which are reversible with respect to Poisson point processes with constant density. For these models, a rate of convergence was recently obtained…
This paper presents a numerical method to implement the parameter estimation method using response statistics that was recently formulated by the authors. The proposed approach formulates the parameter estimation problem of It\^o drift…
In this paper the filtering of partially observed diffusions, with discrete-time observations, is considered. It is assumed that only biased approximations of the diffusion can be obtained, for choice of an accuracy parameter indexed by…
In this paper, we develop an encounter-based model of partial surface adsorption for fractional diffusion in a bounded domain. We take the probability of adsorption to depend on the amount of particle-surface contact time, as specified by a…
We study the properties of a stochastic heat equation with a generalized mixed fractional Brownian noise. We obtain the covariance structure, stationarity and obtain bounds for the asymptotic behaviour of the solution. We suggest estimators…
We study relativistic scattering when one only has access to a subset of the particles, using the language of quantum measurement theory. We give an exact, non-perturbative formula for the von Neumann entanglement entropy of an apparatus…
Inspired by a PDE-ODE system of aggregation developed in the biomathematical literature, an interacting particle system representing aggregation at the level of individuals is investigated. It is proved that the empirical density of the…
We introduce and study interval partition diffusions with Poisson--Dirichlet$(\alpha,\theta)$ stationary distribution for parameters $\alpha\in(0,1)$ and $\theta\ge 0$. This extends previous work on the cases $(\alpha,0)$ and…
We introduce coarse-grained hydrodynamic equations of motion for diffusion-annihilation system with a power-law long-range interaction. By taking into account fluctuations of the conserved order parameter - charge density - we derive an…
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,…
We consider the problem of inferring the interaction kernel of stochastic interacting particle systems from observations of a single particle. We adopt a semi-parametric approach and represent the interaction kernel in terms of a…
Ordinary differential equations (ODEs) are widely used to describe dynamical systems in science, but identifying parameters that explain experimental measurements is challenging. In particular, although ODEs are differentiable and would…