Slepian’s inequality for Gaussian processes with respect to weak majorization

Stochastic Integration with respect to Gaussian Processes

We construct a Stratonovitch-Skorohod-like stochastic integral for general Gaussian processes. We study its sample-paths regularity and one of its numerical approximating schemes. We also analyze the way it is transformed by an absolutely continuous change of probability and we give an Itô formula. c 2001 Académie des sciences/Éditions scientifiques et médicales Elsevier SAS Intégrale stochasti...

Weak Variation of Gaussian Processes

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...

Weak matrix majorization

Given X, Y ∈ Rn×m we introduce the following notion of matrix majorization, called weak matrix majorization, X w Y if there exists a row-stochastic matrix A ∈ Rn×n such that AX = Y, and consider the relations between this concept, strong majorization ( s ) and directional majorization ( ). It is verified that s⇒ ⇒ w , but none of the reciprocal implications is true. Nevertheless, we study the i...

Extermal trees with respect to some versions of Zagreb indices via majorization

The aim of this paper is using the majorization technique to identify the classes of trees with extermal (minimal or maximal) value of some topological indices, among all trees of order n ≥ 12