8 citations · 11 across the 11 of their papers we have counts for
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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(σ_0+σ_1\sqrt{ϕ_\eps(X_t)}\bigr)\,dZ_t^{(q,H)}, \quad X_0 = x_…
Higher-Order Multifractional Stable Motion: Definition and Fundamental Properties
Atef Lechiheb
This paper introduces the -th order multifractional stable motion (-MFSM), a novel stochastic process that simultaneously unifies three key modelling features: heavy-tailed d…
Fractional Navier-Stokes Equations with Caputo Derivative Driven by Hermite Noise
Atef Lechiheb, Lara Daw
We study time-fractional stochastic Navier-Stokes equations on a bounded domain of , driven by a cylindrical Hermite noise of order and Hurst parameter ,…
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 . Using a fixed-point argument in a Malliavin--Sobolev spac…
Concentration of Truncated Signatures of Gaussian Rough Paths
Atef Lechiheb
This paper establishes a comprehensive concentration theory for truncated signatures of Gaussian rough paths. The signature of a path, defined as the collection of all iterated int…
Fractional Homogenization of Parabolic Equations with Long-Range Random Potentials
Atef Lechiheb
This paper establishes a complete homogenization theory for the one-dimensional parabolic equation with long-range correlated random potential: \[ \partial_t u_\varepsilon(t,x) = \…
Canonical Rough Path over Tempered Fractional Brownian Motion: Existence, Construction, and Applications
Atef Lechiheb
We construct a canonical geometric rough path over -dimensional tempered fractional Brownian motion (tfBm) for any Hurst parameter and tempering parameter . The…
Geometric Rough Paths above Mixed Fractional Brownian Motion
Atef Lechiheb
This paper establishes a comprehensive theory of geometric rough paths for mixed fractional Brownian motion (MFBM) and its generalized multi-component extensions. We prove that for…
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 . The equation is formulated in the mild sense using the heat semigroup, and existenc…
Wiener integrals with respect to the two-parameter tempered Hermite random fields
Atef Lechiheb
The two-parameter tempered Hermite field modifies the power law kernel in the moving average representation of the Hermite field by adding an exponential tempering. This paper deve…
Fluctuations in 1D stochastic homogenization of pseudo-elliptic equations with long-range dependent potentials
Atef Lechiheb, Ezeddine Haouala
This paper deals with the homogenization problem of one-dimensional pseudo-elliptic equations with a rapidly varying random potential. The main purpose is to characterize the homog…
Convergence of random oscillatory integrals in the presence of long-range dependence and application to homogenization
Atef Lechiheb, Ivan Nourdin, Guangqu Zheng +1
This paper deals with the asymptotic behavior of random oscillatory integrals in the presence of long-range dependence. As a byproduct, we solve the corrector problem in random hom…