Some Functional Limit Theorems for Dependent Random Variables
Villalobos, Alvaro Gonzalez
Ann. Probab., Tome 2 (1974) no. 6, p. 1090-1107 / Harvested from Project Euclid
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We prove theorems on weak convergence of random elements $X_m(\omega, t), 0 \leqq t \leqq 1$, to a Gaussian process. In Part I, these random elements are constructed on the basis of the linear means of a lacunary trigonometric series $\sum a_j \cos n_j\omega$. In Part II, the lacunarity hypothesis is dropped and replaced by the hypothesis of linear independence of the real numbers $n_j$.
Publié le : 1974-12-14
Classification:  Functional limit theorems for dependent random variables,  Gaussian processes,  lacunary series,  linearly independent numbers,  60F05,  60G15 
@article{1176996500,
     author = {Villalobos, Alvaro Gonzalez},
     title = {Some Functional Limit Theorems for Dependent Random Variables},
     journal = {Ann. Probab.},
     volume = {2},
     number = {6},
     year = {1974},
     pages = { 1090-1107},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1176996500}
}

Villalobos, Alvaro Gonzalez. Some Functional Limit Theorems for Dependent Random Variables. Ann. Probab., Tome 2 (1974) no. 6, pp.  1090-1107. http://gdmltest.u-ga.fr/item/1176996500/