A Maximal Inequality and Dependent Strong Laws
McLeish, D. L.
Ann. Probab., Tome 3 (1975) no. 6, p. 829-839 / Harvested from Project Euclid
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This paper contains a general dependent extension of Doob's inequality for martingales, $E(\max_{i\leqq n} S_i^2) \leqq 4ES_n^2$. This inequality is then used to extend the martingale convergence theorem for $L_2$ bounded variables, and to prove strong laws under dependent assumptions. Strong and $\varphi$-mixing variables are shown to satisfy the conditions of these theorems and hence strong laws are proved as well for these.
Publié le : 1975-10-14
Classification:  Strong law,  martingale convergence theorem,  dependent variables,  Doob's inequality,  mixing,  60F15,  60G45 
@article{1176996269,
     author = {McLeish, D. L.},
     title = {A Maximal Inequality and Dependent Strong Laws},
     journal = {Ann. Probab.},
     volume = {3},
     number = {6},
     year = {1975},
     pages = { 829-839},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1176996269}
}

McLeish, D. L. A Maximal Inequality and Dependent Strong Laws. Ann. Probab., Tome 3 (1975) no. 6, pp.  829-839. http://gdmltest.u-ga.fr/item/1176996269/