Bipower variation for Gaussian processes with stationary increments

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...

The Rate of Entropy for Gaussian Processes

In this paper, we show that in order to obtain the Tsallis entropy rate for stochastic processes, we can use the limit of conditional entropy, as it was done for the case of Shannon and Renyi entropy rates. Using that we can obtain Tsallis entropy rate for stationary Gaussian processes. Finally, we derive the relation between Renyi, Shannon and Tsallis entropy rates for stationary Gaussian proc...

Representations of Gaussian processes with stationary increments

Growth Rate of Certain Gaussian Processes

We will be concerned with real, continuous Gaussian processes. In (A) of Theorem 1.1, a result on the growth rate of the supremum as t oo is given. The processes covered by Theorem 1.1 all have stationary increments. The law of the iterated logarithm, given as (C) below, is a consequence of (A). Theorem 1.1 will be stated and discussed in this section. The proof of this theorem and supporting p...

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...