We study here explicit flux-splitting finite volume discretizations of multi-dimensional nonlinear scalar conservation laws perturbed by a multiplicative noise with a given initial data in L(R). Under a stability condition on the time step, we prove the convergence of the finite volume approximation towards the unique stochastic entropy solution of the equation.

Constructing discrete models of stochastic partial differential equations is very delicate. Here we describe how stochastic centre manifold theory provides novel support for spatial discretisations of the nonlinear advection-diffusion dynamics of the stochastically forced Burgers’ equation. Dividing the physical domain into finite sized elements empowers the approach to resolve fully coupled dy...

This paper focuses on the problem of multiplicative noise removal. We draw our inspiration from the modeling of speckle noise. By using a MAP estimator, we can derive a functional whose minimizer corresponds to the denoised image we want to recover. Although the functional is not convex, we prove the existence of a minimizer and we show the capability of our model on some numerical examples. We...

We prove that an averaging principle holds for a general class of stochastic reactiondiffusion systems, having unbounded multiplicative noise, in any space dimension. We show that the classical Khasminskii approach for systems with a finite number of degrees of freedom can be extended to infinite dimensional systems.

In this paper, we introduce a simple reweighted residual-feedback iterative (RRFI) algorithmwhich provides a general framework to solve the fractional-order total variation regularized models with different fidelity terms. We provide a sufficient condition for the convergence of this algorithm. As an application, we use this algorithm to solve the TV and fractional-order TV regularized models w...

We introduce a class of numerical methods for highly oscillatory systems of stochastic differential equations with general noncommutative noise. We prove global weak error bounds of order two uniformly with respect to the stiffness of the oscillations, which permits to use large time steps. The approach is based on the micro-macro framework of multi-revolution composition methods recently intro...

We report on-off intermittency in electroconvection of nematic liquid crystals driven by a dichotomous stochastic electric voltage. Above DC threshold with increasing voltage amplitude we observe laminar phases of undistorted director state interrupted by shorter bursts of regular stripes. Near a critical value of the amplitude the distribution of the duration of laminar phases is governed over...

In this paper an approximate innovation method is introduced for the estimation of diffusion processes given a set of discrete and noisy observations of some of their components. The method is based on a recent extension of Local Linearization filters to the general case of continuous-discrete state space models with multiplicative noise. This filtering method provides adequate approximations f...

A non symmetric version of Hopfield networks subject to state-multiplicative noise, pure time delay and Markov jumps is considered. Such networks seem to arise in the context of visuo-motor control loops and may, therefore, be used to mimic their complex behaviour. In this paper, we adopt the Lur’e-Postnikov systems approach to analyze the stochastic stability and the L2 gain of generalized Hop...

We study existence and uniqueness of a mild solution in the space of continuous functions and existence of an invariant measure for a class of reaction-diffusion systems on bounded domains of R , perturbed by a multiplicative noise. The reaction term is assumed to have polynomial growth and to be locally Lipschitz-continuous and monotone. The noise is white in space and time if d = 1 and colour...