Research ArticleOpen accessIn the keywordsLimit Theorems for a Class of Additive Functionals of Symmetric Stable Process and Fractional Brownian Motion in Besov-Orlicz SpacesM. Ait Ouahra, A. Kissami, A. SghirWe use the Potter's Theorem and the tightness criterion in Besov-Orlicz spaces, recently proved, to generalize some limit theorem for occupation times problem of certain self-similar process, namely symmetric stable process of index 1<α≤ and fractional Brownian motion of Hurst parameter 0<H<1. We give also strong approximation version of our limit theorem, more precisely, we show Lp-estimate version. …Journal of Mathematics and Statistics, Vol. 8, Issue 4 · 22 Feb 2013 · 6,757 accessesView PDFCite
Research ArticleOpen accessIn the abstractA Convergence Theorem for Bivariate Exponential Dispersion ModelsLila Ricci, Gabriela BoggioMultivariate exponential dispersion models (MEDMs) were defined in 2013 by Jørgensen and Martínez. A particular case of MEDM is the bivariate Gamma model; in this article we prove that, under certain conditions, this is a limit distribution for MEDM generated by bivariate regularly varying measures, extending a previous result given by the aforementioned authors for the univariate case. As necessary … …Journal of Mathematics and Statistics, Vol. 15, Issue 1 · 25 Jul 2019 · 6,582 accessesView PDFCite