相关论文: Benchmark solutions for transport in $d$-dimension…

Markov chain Monte Carlo methods have become standard tools in statistics to sample from complex probability measures. Many available techniques rely on discrete-time reversible Markov chains whose transition kernels build up over the…

This paper addresses distributed parameter estimation in stochastic dynamic systems with quantized measurements, constrained by quantized communication and Markovian switching directed topologies. To enable accurate recovery of the original…

This article deals with transport properties of one dimensional Brownian diffusion under the influence of a correlated quenched random force, distributed as a two-level Poisson process. We find in particular that large time scaling laws of…

Different techniques of event biasing have been implemented in the particle-based Monte Carlo simulations of a 15nm n-channel MOSFET. The primary goal is to achieve enhancement in the channel statistics and faster convergence in the…

A diffusion taking value in probability measures on a graph with a vertex set $V$, $\sum_{i\in V}x_i\delta_i$, is studied. The masses on each vertices satisfy the stochastic differential equation of the form $dx_i=\sum_{j\in…

We consider a discrete-time system of n coupled random vectors, a.k.a. interacting particles. The dynamics involve a vanishing step size, some random centered perturbations, and a mean vector field which induces the coupling between the…

Monte Carlo (MC) simulations allowing to describe photons propagation in statistical mixtures represent an interest that goes way beyond the domain of optics, and can cover, e.g., nuclear reactor physics, image analysis or life science just…

Accurate determination of carrier transport properties in two-dimensional (2D) materials is critical for designing high-performance nano-electronic devices and quantum information platforms. While first-principles calculations effectively…

In this paper we show that we can use Markov kernels as a model for optimal transport. This new framework can be easily translated into the standard coupling formulation of optimal transport, and we show that we can use a coupling as a…

Stochastic difference equations and a stochastic partial differential equation (SPDE) are simultaneously derived for the time-dependent neutron angular density in a general three-dimensional medium where the neutron angular density is a…

The paper studies the optimal density steering problem for nonlinear continuous-time stochastic systems. To accurately capture nonlinear dynamics in high-uncertainty regions that deviate significantly from a nominal linearization point, we…

We consider the stochastic target problem of finding the collection of initial laws of a mean-field stochastic differential equation such that we can control its evolution to ensure that it reaches a prescribed set of terminal probability…

We consider a high-dimensional mean estimation problem over a binary hidden Markov model, which illuminates the interplay between memory in data, sample size, dimension, and signal strength in statistical inference. In this model, an…

We study the limiting spectral distribution of large-dimensional sample covariance matrices associated with symmetric random tensors formed by $\binom{n}{d}$ different products of $d$ variables chosen from $n$ independent standardized…

Transporting between arbitrary distributions is a fundamental goal in generative modeling. Recently proposed diffusion bridge models provide a potential solution, but they rely on a joint distribution that is difficult to obtain in…

Pointwise accurate numerical methods are constructed and analysed for three classes of singularly perturbed first order transport problems. The methods involve piecewise-uniform Shishkin meshes and the numerical approximations are shown to…

We show how the nonlinear interaction effects `volume filling' and `adhesion' can be incorporated into the fractional subdiffusive transport of cells and individual organisms. To this end, we use microscopic random walk models with…

This paper builds on recent developments of adaptive methods for linear transport equations based on certain stable variational formulations of Petrov-Galerkin type. The variational formulations allow us to employ meshes with cells of…

We consider particles that are conditioned to initial and final states. The trajectory of these particles is uniquely shaped by the intricate interplay of internal and external sources of randomness. The internal randomness is aptly…

We consider the Poisson-Nernst-Planck system which is well-accepted for describing dilute electrolytes as well as transport of charged species in homogeneous environments. Here, we study these equations in porous media whose electric…