Almost sure limit theorems for dependent random variables
Michał Seweryn
Banach Center Publications, Tome 89 (2010), p. 171-178 / Harvested from The Polish Digital Mathematics Library
Access to full text
Full (PDF)

For a sequence of dependent random variables (Xk)k∈ℕ we consider a large class of summability methods defined by R. Jajte in [jaj] as follows: For a pair of real-valued nonnegative functions g,h: ℝ⁺ → ℝ⁺ we define a sequence of “weighted averages” 1/g(n)∑k=1n(Xk)/h(k), where g and h satisfy some mild conditions. We investigate the almost sure behavior of such transformations. We also take a close look at the connection between the method of summation (that is the pair of functions (g,h)) and the coefficients that measure dependence between the random variables.

Publié le : 2010-01-01
EUDML-ID : urn:eudml:doc:282542 
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-bc90-0-11,
     author = {Micha\l\ Seweryn},
     title = {Almost sure limit theorems for dependent random variables},
     journal = {Banach Center Publications},
     volume = {89},
     year = {2010},
     pages = {171-178},
     zbl = {1210.60032},
     language = {en},
     url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-bc90-0-11}
}

Michał Seweryn. Almost sure limit theorems for dependent random variables. Banach Center Publications, Tome 89 (2010) pp. 171-178. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-bc90-0-11/