Gaussian processes with stationary increments possessing discontinuous sample paths

Representations of Gaussian processes with stationary increments

Bipower variation for Gaussian processes with stationary increments

Convergence in probability and central limit laws of bipower variation for Gaussian processes with stationary increments and for integrals with respect to such processes are derived. The main tools of the proofs are some recent powerful techniques of Wiener/Itô/Malliavin calculus for establishing limit laws, due to Nualart, Peccati and others.

Growth Rate of Gaussian Processes with Stationary Increments

Communicated by David Blackwell, November 3, 1969 1. Statement of results. Let (Y, «, t^O) be a real, separable Gaussian process with stationary increments, mean 0, and F0 = 0. Let 2Q(t) be the variance of Yt and define Xt = Yt/(2Q(t)yi\ THEOREM 1. Suppose there exists a nonnegative function v(t) such that Q(s + t) Q(s) (*) lim = 1 uniformly in s t~*oo v(s + 0 "~ () and there exist positive con...

Power variation for Gaussian processes with stationary increments ∗

We develop the asymptotic theory for the realised power variation of the processes X = φ • G, where G is a Gaussian process with stationary increments. More specifically, under some mild assumptions on the variance function of the increments of G and certain regularity condition on the path of the process φ we prove the convergence in probability for the properly normalised realised power varia...

Simulation of Sample Paths of Non Gaussian Stationary Random Fields

Mathematical justifications are given for a simulation technique of multivariate nonGaussian random processes and fields based on Rosenblatt’s transformation of Gaussian processes. Different types of convergences are given for the approaching sequence. Moreover an original numerical method is proposed in order to solve the functional equation yielding the underlying Gaussian process autocorrela...