arXiv subjects

A. Stavrianidi

Publications and source records attributed to A. Stavrianidi.

3 recordsLinked to original sources

arXiv2024

Malliavin Calculus for the stochastic heat equation and results on the density

We study the one-dimensional stochastic heat equation with unbounded, nonlinear,Lipschitz coefficients with Dirichlet boundary conditions. Using Malliavin calculus, we construct a piecewise approximation of the solution u and establish regularity results. This approximation enables us to provide a new proof of the existence of a density for the random variable u(t, x) at any fixed t, x. Unlike existing proofs, which rely on comparison principles ([10], [12]), our approach is based purely on a localization argument, which allows us to handle the unbounded coefficients.

math.AP↗

arXiv2019

Algebraic genericity of frequently universal harmonic functions on trees

We show that the set of frequently universal harmonic functions on a tree T contains a vector space except 0 which is dense in the space of harmonic functions on T seen as subset of C^T . In order to prove this we replace the complex plane C by any separable Frechet space E and we repeat all the theory.

math.FA↗

arXiv2018

Generic non-extendability and total unboundedness in function spaces

For a function space $X(\OO)$ satisfying weak assumptions we prove that the generic function in $X(\OO)$ is totally unbounded, hence non-extendable. We provide several examples of such spaces; they are mainly localized versions of classical function spaces and intersections of them.

math.CV↗