On Convergence in $r$-Mean of Normalized Partial Sums
Dharmadhikari, S. W. ; Sreehari, M.
Ann. Probab., Tome 3 (1975) no. 6, p. 1023-1024 / Harvested from Project Euclid
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Suppose $S_n = \sum^n_1 X_j$, where $\{X_n\}$ is a sequence of random variables. Under progressively weaker hypotheses, Pyke and Root (1968), Chatterji (1969) and Chow (1971) have proved that $E|S_n - b_n|^r = o(n)$, where $0 < r < 2$ and $\{b_n\}$ is properly chosen. This paper gives a fairly elementary proof of Chow's result under further weakened hypotheses.
Publié le : 1975-12-14
Classification:  $r$-mean convergence,  martingales,  60F15,  60G45 
@article{1176996228,
     author = {Dharmadhikari, S. W. and Sreehari, M.},
     title = {On Convergence in $r$-Mean of Normalized Partial Sums},
     journal = {Ann. Probab.},
     volume = {3},
     number = {6},
     year = {1975},
     pages = { 1023-1024},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1176996228}
}

Dharmadhikari, S. W.; Sreehari, M. On Convergence in $r$-Mean of Normalized Partial Sums. Ann. Probab., Tome 3 (1975) no. 6, pp.  1023-1024. http://gdmltest.u-ga.fr/item/1176996228/