5 papers
Malliavin calculus and densities for chaos-driven stochastic differential equations
Laurent Loosveldt, Yassine Nachit, Ivan Nourdin
We study stochastic differential equations driven by finite-order chaos processes on abstract Wiener spaces, with pathwise Riemann-Stieltjes integration. The driving noise is an $\…
Quartic variation of the solution to the semilinear stochastic heat equation: limit behavior and asymptotic independence with respect to the data
I Cîmpean, Yassine Nachit, Ciprian A Tudor
This work concerns the limit behavior of the quartic variation (i.e., the power variation of order four) with respect to the time variable of the solution to the semilinear stochas…
Malliavin smoothness of the Rosenblatt process
Laurent Loosveldt, Yassine Nachit, Ivan Nourdin +1
We investigate the smoothness of the densities of the finite-dimensional distributions of the Rosenblatt process. Within the Malliavin calculus framework, we prove that Rosenblatt…
Absolute continuity of finite-dimensional distributions of Hermite processes via Malliavin calculus
Laurent Loosveldt, Yassine Nachit, Ivan Nourdin +1
We investigate the existence of densities for finite-dimensional distributions of Hermite processes of order \(q \ge 1\) and self-similarity parameter \(H\in(\frac12,1)\). Whereas…
On the uniform Besov regularity of local times of general processes
Brahim Boufoussi, Yassine Nachit
Our main purpose is to use a new condition, -local nondeterminism, which is an alternative to the classical local nondeterminism usually utilized in the Gaussian framework, in…