Estimation of ordinal pattern probabilities in Gaussian processes with stationary increments

Lower Tail Probabilities for Gaussian Processes

Let X = (Xt )t∈S be a real-valued Gaussian random process indexed by S with mean zero. General upper and lower estimates are given for the lower tail probability P(supt∈S(Xt − Xt0) ≤ x) as x → 0, with t0 ∈ S fixed. In particular, sharp rates are given for fractional Brownian sheet. Furthermore, connections between lower tail probabilities for Gaussian processes with stationary increments and le...

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.

Representations of Gaussian processes with stationary increments

Efficient Parameter Estimation for Self - Similar Processes

In the paper [1] the author claimed to have established asymptotic normality and efficiency of the Gaussian maximum likelihood estimator (MLE) for long range dependent processes (with the increments of the self-similar fractional Brownian motion as a special case—hence, the title of the paper). The case considered in the paper was Gaussian stationary sequences with spectral densities fθ(x)∼ |x|...