Growth Rate 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...

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...

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.

ADK Entropy and ADK Entropy Rate in Irreducible- Aperiodic Markov Chain and Gaussian Processes

In this paper, the two parameter ADK entropy, as a generalized of Re'nyi entropy, is considered and some properties of it, are investigated. We will see that the ADK entropy for continuous random variables is invariant under a location and is not invariant under a scale transformation of the random variable. Furthermore, the joint ADK entropy, conditional ADK entropy, and chain rule of this ent...

Representations of Gaussian processes with stationary increments