On weighted approximations in $D[0, 1]$ with applications to self-normalized partial sum processes

dc.creatorCsörgő, Miklós
dc.creatorSzyszkowicz, Barbara
dc.creatorWang, Qiying
dc.date2007-11-09
dc.date.accessioned2026-07-07T08:41:50Z
dc.date.available2026-07-07T08:41:50Z
dc.descriptionLet $X, X_1, X_2,...$ be a sequence of non-degenerate i.i.d. random variables with mean zero. The best possible weighted approximations are investigated in $D[0, 1]$ for the partial sum processes $\{S_{[nt]}, 0\le t\le 1\}$, where $S_n=\sum_{j=1}^nX_j$, under the assumption that $X$ belongs to the domain of attraction of the normal law. The conclusions then are used to establish similar results for the sequence of self-normalized partial sum processes $\{S_{[nt]}/V_n, 0\le t\le 1\}$, where $V_n^2=\sum_{j=1}^nX_j^2$. $L_p$ approximations of self-normalized partial sum processes are also discussed.
dc.description22 pages
dc.identifierhttps://arxiv.org/abs/0711.1384
dc.identifierhttp://arxiv.org/abs/0711.1384
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/141798
dc.subjectProbability
dc.subject60G50, 60F17, 60F25 (Primary); 62E20 (Secondary)
dc.titleOn weighted approximations in $D[0, 1]$ with applications to self-normalized partial sum processes
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