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Stochastic differential equations provide a powerful tool for modelling dynamic phenomena affected by random noise. In case of repeated observations of time series for several experimental units, it is often the case that some of the…
One-dimensional stochastic differential equations with additive L\'evy noise are considered. Conditions for existence and uniqueness of a strong solution are obtained. In particular, if the noise is a L\'evy symmetric stable process with…
This paper investigates the two-dimensional stochastic steady-state Navier-Stokes(NS) equations with additive random noise. We introduce an innovative splitting method that decomposes the stochastic NS equations into a deterministic NS…
Stochastic inverse problems considered in this article consist of estimating the probability distributions of intrinsically random inputs of computer models. These estimations are based on observable outputs affected by model noise, and…
We analyse the non-equilibrium distribution in dissipative dynamical systems at finite noise intensities. The effect of finite noise is described in terms of topological changes in the pattern of optimal paths. Theoretical predictions are…
We survey some of our recent results on existence, uniqueness and regularity of function solutions to parabolic and transport type partial differential equations driven by non-differentiable noises. When applied pathwise to random…
We establish the existence and uniqueness of strong solutions, in both the PDE and probabilistic sense, for a broad class of nonlinear stochastic partial differential equations (SPDEs) on a bounded domain $\mathscr{O}\subset \mathbb{R}^d$…
Several aspects of regularity theory for parabolic systems are investigated under the effect of random perturbations. The deterministic theory, when strict parabolicity is assumed, presents both classes of systems where all weak solutions…
We study distribution dependent stochastic differential equation driven by a continuous process, without any specification on its law, following the approach initiated in [16]. We provide several criteria for existence and uniqueness of…
We introduce and analyse an individual-based evolutionary model, in which a population of genetically diverse organisms compete with each other for limited resources. Through theoretical analysis and stochastic simulations, we show that the…
The deterministic inviscid primitive equations (also called the hydrostatic Euler equations) are known to be ill-posed in Sobolev spaces and in Gevrey classes of order strictly greater than 1, and some of their analytic solutions exist only…
This work develops a quantitative homogenization theory for random suspensions of rigid particles in a steady Stokes flow, and completes recent qualitative results. More precisely, we establish a large-scale regularity theory for this…
We investigate the stabilization of unstable multidimensional partially observed single-sensor and multi-sensor linear systems driven by unbounded noise and controlled over discrete noiseless channels under fixed-rate information…
This paper studies the nonlinear one-dimensional stochastic heat equation driven by a Gaussian noise which is white in time and which has the covariance of a fractional Brownian motion with Hurst parameter 1/4\textless{}H\textless{}1/2 in…
On the one hand, we investigate the existence and pathwise uniqueness of a nonnegative martingale solution to the stochastic evolution system of nonlinear advection-diffusion equations proposed by Klausmeier with Gaussian multiplicative…
Fokker-Planck equations describe time evolution of probability densities of stochastic dynamical systems and play an important role in quantifying propagation and evolution of uncertainty. Although Fokker-Planck equations can be written…
Stochastic-periodic homogenization is studied for the Maxwell equations with nonlinear and periodic electric conductivity. It is shown by the stochastic-two-scale convergence method that the sequence of solutions of a class of highly…
A system of interacting particles described by stochastic differential equations is considered. As oppopsed to the usual model, where the noise perturbations acting on different particles are independent, here the particles are subject to…
Stochastic Approximation has been a prominent set of tools for solving problems with noise and uncertainty. Increasingly, it becomes important to solve optimization problems wherein there is noise in both a set of constraints that a…
We study the convergence of a Zakharov system driven by a time white noise, colored in space, to a multiplicative stochastic nonlinear Schr{\"o}dinger equation, as the ion-sound speed tends to infinity. In the absence of noise, the…