Atef Lechiheb

collaborators

9 papers

math.PR2026

A CIR-Type Diffusion Driven by Hermite Processes: Well-Posedness, Positivity and Malliavin Analysis

Atef Lechiheb

We study a generalized Cox--Ingersoll--Ross (CIR) diffusion \begin{equation*} dX_t = a\bigl(b(t)-X_t\bigr)\,dt + \bigl(Ï_0+Ï_1\sqrt{Ï_\eps(X_t)}\bigr)\,dZ_t^{(q,H)}, \quad X_0 =…

math.PR2026

Higher-Order Multifractional Stable Motion: Definition and Fundamental Properties

Atef Lechiheb

This paper introduces the $n$ -th order multifractional stable motion ( $n$ -MFSM), a novel stochastic process that simultaneously unifies three key modelling features: heavy-tailed d…

math.PR2026

Stochastic Burgers Equation Driven by a Hermite Sheet with Additive Noise: Existence, Uniqueness, and Regularity

Atef Lechiheb

We study the stochastic Burgers equation driven by an additive Hermite sheet of order $q \geq 1$ . The equation is formulated in the mild sense using the heat semigroup, and existenc…

math.PR2026

Canonical Rough Path over Tempered Fractional Brownian Motion: Existence, Construction, and Applications

Atef Lechiheb

We construct a canonical geometric rough path over $d$ -dimensional tempered fractional Brownian motion (tfBm) for any Hurst parameter $H > 1/4$ and tempering parameter $I^» > 0$ . The…

math.PR2026

Fractional Navier-Stokes Equations with Caputo Derivative Driven by Hermite Noise

Atef Lechiheb

We study time-fractional stochastic Navier-Stokes equations on a bounded domain of $R^{2}$ (the restriction to dimension two is essential for the bilinear estimates via Sobolev embe…

math.PR2026

Stochastic Burgers equation driven by multiplicative Rosenblatt noise: local existence, uniqueness and regularity

Atef Lechiheb

We study the stochastic Burgers equation driven by a multiplicative Rosenblatt noise with Hurst parameter $H \in (1/2, 1)$ . Using a fixed-point argument in a Malliavin--Sobolev spac…