4 papers
Modified weighted power variations of the Hermite process and applications to integrated volatility
Antoine Ayache, laurent Loosveldt, Ciprian Tudor
We study the asymptotic behaviour of modified weighted power variations of the Hermite process of arbitrary order. By selecting suitable "good" increments and exploiting their deco…
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…