Local martingale and pathwise solutions for an abstract fluids model
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 …
solutions of an abstract nonlinear stochastic evolution system. The primary application of this …
Data-driven non-Markovian closure models
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 …
models by using a multivariate time series of partial observations from a large-dimensional …
[HTML][HTML] Hybrid monte carlo on hilbert spaces
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 …
high-dimensional target distributions. In contrast with standard Markov chain Monte Carlo …
Well-posedness and accuracy of the ensemble Kalman filter in discrete and continuous time
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 …
with data in a sequential fashion. Despite its widespread use, there has been little analysis …
Positivity-preserving consensus of homogeneous multiagent systems
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 …
multiagent systems. The case that all agents have identical positive state-space models with …
[HTML][HTML] Degenerate parabolic stochastic partial differential equations
M Hofmanová - Stochastic Processes and their Applications, 2013 - Elsevier
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 …
differential equation with stochastic forcing. In particular, we are concerned with the well …
Sampling the posterior: An approach to non-Gaussian data assimilation
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 …
problem and that this problem should be cast in a Bayesian framework. In the absence of …
[HTML][HTML] Strong and weak orders in averaging for SPDEs
CE Bréhier - Stochastic Processes and their Applications, 2012 - Elsevier
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 …
with slow and fast time scales. We derive explicit bounds for the approximation error with …
[HTML][HTML] Strong convergence rates for nonlinearity-truncated Euler-type approximations of stochastic Ginzburg–Landau equations
S Becker, A Jentzen - Stochastic Processes and their Applications, 2019 - Elsevier
This article proposes and analyzes explicit and easily implementable temporal numerical
approximation schemes for additive noise-driven stochastic partial differential equations …
approximation schemes for additive noise-driven stochastic partial differential equations …
Ergodicity results for the stochastic Navier–Stokes equations: an introduction
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 …
advances those last 20 years. Existence and uniqueness have been studied in various …