Information Theory for Non-Stationary Processes with Stationary Increments

Representations of Gaussian processes with stationary increments

Minimax Interpolation Problem for Random Processes with Stationary Increments

The problem of mean-square optimal estimation of the linear functional AT ξ = ∫ T 0 a(t)ξ(t)dt that depends on the unknown values of a continuous time random process ξ(t), t ∈ R, with stationary nth increments from observations of the process ξ(t) at time points t ∈ R \ [0;T ] is investigated under the condition of spectral certainty as well as under the condition of spectral uncertainty. Formu...

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.

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...

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...