4 papers · 1 filter
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 $\…
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…
Numerical simulation of Generalized Hermite Processes
Antoine Ayache, Julien Hamonier, laurent Loosveldt
Hermite processes are paradigmatic examples of stochastic processes which can belong to any Wiener chaos of an arbitrary order; the wellknown fractional Brownian motion belonging t…