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Lahcen Boulanba

Publications and source records attributed to Lahcen Boulanba.

5 recordsLinked to original sources
arXiv2025

On Malliavin differentiability and absolute continuity of one-dimensional doubly perturbed diffusion processes

In this paper, we establish Malliavin differentiability and absolute continuity for $α, β$-doubly perturbed diffusion process with parameters $α<1$ and $β<1$ such that $|ρ| < 1$, where $ ρ: = \frac{αβ}{(1-α)(1-β)}$. Furthermore, under some regularity conditions on the coefficients, we prove that the solution $X_t$ has a smooth density for all $t\in(0, t_0)$ for some finite number $t_0>0$. Our results recover earlier works by Yue and Zhang (2015) and Xue, Yue and Zhang (2016), and the proofs are based on the techniques of the Malliavin calculus.

math.PR↗
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↗
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↗