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Interacting particle methods are increasingly used to sample from complex and high-dimensional distributions. These stochastic particle integration techniques can be interpreted as an universal acceptance-rejection sequential particle…
We study the stochastic diffusive limit of a kinetic radiative transfer equation, which is non-linear, involving a small parameter and perturbed by a smooth random term. Under an appropriate scaling for the small parameter, using a…
This paper derives a \emph{distributed} Kalman filter to estimate a sparsely connected, large-scale, $n-$dimensional, dynamical system monitored by a network of $N$ sensors. Local Kalman filters are implemented on the ($n_l-$dimensional,…
We discuss application of methods from the Kraichnan model of turbulent advection to the study of non-equilibrium concentration fluctuations arising during diffusion in liquid mixtures at high Schmidt numbers. This approach treats nonlinear…
Matrix-valued stochastic processes have been of significant importance in areas such as physics, engineering and mathematical finance. One of the first models studied has been the so-called Wishart process, which is described as the…
This paper is devoted the the study of the mean field limit for many-particle systems undergoing jump, drift or diffusion processes, as well as combinations of them. The main results are quantitative estimates on the decay of fluctuations…
We develop stochastic mixed finite element methods for spatially adaptive simulations of fluid-structure interactions when subject to thermal fluctuations. To account for thermal fluctuations, we introduce a discrete fluctuation-dissipation…
Field theory tools are applied to analytically study fluctuation and correlation effects in spatially extended stochastic predator-prey systems. In the mean-field rate equation approximation, the classic Lotka-Volterra model is…
The inference of causal relationships among observed variables is a pivotal, longstanding problem in the scientific community. An intuitive method for quantifying these causal links involves examining the response of one variable to…
We propose a model of random diffusion to investigate flow fluctuations in complex networks. We derive an analytical law showing that the dependence of fluctuations with the mean traffic in a network is ruled by the delicate interplay of…
Many biological activities are induced by cellular chemical reactions of diffusing reactants. The dynamics of such systems can be captured by stochastic reaction networks. A recent numerical study has shown that diffusion can significantly…
This paper proposes a fully data-driven approach for optimal control of nonlinear control-affine systems represented by a stochastic diffusion. The focus is on the scenario where both the nonlinear dynamics and stage cost functions are…
We investigate coupled stochastic differential equations governing N non-negative continuous random variables that satisfy a conservation principle. In various fields a conservation law requires that a set of fluctuating variables be…
We investigate the propagation of random fluctuations through biochemical networks in which the concentrations of species are large enough so that the unperturbed problem is well-described by ordinary differential equation. We characterize…
This paper proposes a novel iterative algorithm to compute the stabilizing solution of regime-switching stochastic game-theoretic Riccati differential equations with periodic coefficients. The method decomposes the original complex…
Stochastic models of diffusion with excluded-volume effects are used to model many biological and physical systems at a discrete level. The average properties of the population may be described by a continuum model based on partial…
In this contribution we consider stochastic growth models in the Kardar-Parisi-Zhang universality class in 1+1 dimension. We discuss the large time distribution and processes and their dependence on the class on initial condition. This…
Understanding particle motion in narrow channels is essential to guide progress in numerous applications, from filtration to vascular transport. Thermal or active fluctuations of channel walls for fluid-filled channels can slow down or…
We discuss recently discovered links of the statistical models of normal random matrices to some important physical problems of pattern formation and to the quantum Hall effect. Specifically, the large $N$ limit of the normal matrix model…
The relation between relaxation and diffusion is investigated in a Hamiltonian system of globally coupled rotators. Diffusion is anomalous if and only if the system is going towards equilibrium. The anomaly in diffusion is not anomalous…