We establish the existence and uniqueness of both local martingale and local pathwise
solutions of an abstract nonlinear stochastic evolution system. The primary application of this …

This paper has two interrelated foci:(i) obtaining stable and efficient data-driven closure
models by using a multivariate time series of partial observations from a large-dimensional …

The Hybrid Monte Carlo (HMC) algorithm provides a framework for sampling from complex,
high-dimensional target distributions. In contrast with standard Markov chain Monte Carlo …

Abstract The ensemble Kalman filter (EnKF) is a method for combining a dynamical model
with data in a sequential fashion. Despite its widespread use, there has been little analysis …

This note deals with the positivity-preserving consensus problem for undirected positive
multiagent systems. The case that all agents have identical positive state-space models with …

We study the Cauchy problem for a scalar semilinear degenerate parabolic partial
differential equation with stochastic forcing. In particular, we are concerned with the well …

The viewpoint taken in this paper is that data assimilation is fundamentally a statistical
problem and that this problem should be cast in a Bayesian framework. In the absence of …

We show an averaging result for a system of stochastic evolution equations of parabolic type
with slow and fast time scales. We derive explicit bounds for the approximation error with …

This article proposes and analyzes explicit and easily implementable temporal numerical
approximation schemes for additive noise-driven stochastic partial differential equations …

The theory of the stochastic Navier–Stokes equations (SNSE) has known a lot of important
advances those last 20 years. Existence and uniqueness have been studied in various …