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Mohamed Mellouk

Publications and source records attributed to Mohamed Mellouk.

8 recordsLinked to original sources
arXiv2024

The robusTest package: two-sample tests revisited

The R package robusTest offers corrected versions of several common tests in bivariate statistics. We point out the limitations of these tests in their classical versions, some of which are well known such as robustness or calibration problems, and provide simple alternatives that can be easily used instead. The classical tests and theirs robust alternatives are compared through a small simulation study. The latter emphasizes the superiority of robust versions of the test of interest. Finally, an illustration of correlation's tests on a real data set is also provided.

stat.ME↗
arXiv2017

Large deviations for a stochastic Cahn-Hilliard equation in Hölder norm

We consider a stochastic Cahn-Hilliard partial differential equation driven by a space-time white noise. We prove the Large Deviations Principle (LDP) for the law of the solutions in the Hölder norm. We use the weak convergence approach that reduces the proof to establishing basic qualitative properties for controlled analogues of the original stochastic system.

math.PR↗
arXiv2015

Large deviations for a fractional stochastic heat equation in spatial dimension $\mathbb{R}^d$ driven by a spatially correlated noise

In this paper we study the Large Deviation Principle (LDP in abbreviation) for a class of Stochastic Partial Differential Equations (SPDEs) in the whole space $\mathbb{R}^d$, with arbitrary dimension $d\geq 1$, under random influence which is a Gaussian noise, white in time and correlated in space. The differential operator is a fractional derivative operator. We prove a large deviations principle for our equation, using a weak convergence approach based on a variational representation of functionals of infinite-dimensional Brownian motion. This approach reduces the proof of LDP to establishing basic qualitative properties for controlled analogues of the original stochastic system.

math.PR↗
arXiv2011

On a high-dimensional nonlinear stochastic partial differential equation

In this paper we investigate a nonlinear stochastic partial differential equation (spde in short) perturbed by a space-correlated Gaussian noise in arbitrary dimension $d\geq1$, with a non-Lipschitz coefficient noisy term. The equation studied coincides in one dimension with the stochastic Burgers equation. Existence of a weak solution is established through an approximation procedure.

math.PR↗
arXiv2006

Fractional SPDEs driven by spatially correlated noise: existence of the solution and smoothness of its density

In this paper we study a class of stochastic partial differential equations in the whole space $\mathbb{R}^{d}$, with arbitrary dimension $d\geq 1$, driven by a Gaussian noise white in time and correlated in space. The differential operator is a fractional derivative operator. We show the existence, uniqueness and Hölder's regularity of the solution. Then by means of Malliavin calculus, we prove that the law of the solution has a smooth density with respect to the Lebesgue measure.

math.PR↗