3 papers
math.PR2025
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…
math.PR2025
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) = \…
math.PR2025
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…