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…