We establish weak convergence of partial sums of tempered fractional time series (TFTS) to a stochastic process which we call a tempered Gaussian Hermite process (TGHP). We also introduce the Wiener integral with respect to TGHP, and establish weak convergence of weighted sums of TFTS to this Wiener integral.

In this paper, we consider a d-dimensional continuous Itô process which is observed at n regularly spaced times on a given time interval [0, T ]. This process is driven by a multidimensional Wiener process and our aim is to provide asymptotic statistical procedures which give the minimal dimension of the driving Wiener process, which is between 0 (a pure drift) and d. We exhibit several differe...

neural networks are applicable in identification systems from input-output data. in this report, we analyze thehammerstein-wiener models and identify them. thehammerstein-wiener systems are the simplest type of block orientednonlinear systems where the linear dynamic block issandwiched in between two static nonlinear blocks, whichappear in many engineering applications; the aim of nonlinearsyst...

In this paper, we consider the Lévy Laplacian acting on multiple Wiener integrals by the Lévy process, and give a necessary and sufficient condition for eigenfunctions of the Lévy Laplacian. Moreover we give a decomposition by eigenspaces consisting of multiple Wiener integrals by the Lévy process in terms of the Lévy Laplacian.