8 citations · 11 across the 11 of their papers we have counts for
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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…