Geodesic
On the Maximal Lévy–Ottaviani Inequality for Sums of Independent and Dependent Random Vectors
Zbigniew S. Szewczak1
1 Faculty of Mathematics and Computer Science Nicolaus Copernicus University 87-100 Toruń, Poland
Bulletin of the Polish Academy of Sciences. Mathematics, Tome 61 (2013) no. 2, pp. 155-160

Voir la notice de l'article provenant de la source Institute of Mathematics Polish Academy of Sciences

We prove that the sums $S_k$ of independent random vectors satisfy \[ P\left(\max_{1\leq k\leq n} \| S_k\| > 3t\right) \leq 2\max_{1\leq k\leq n} P(\|S_k\| > t),\quad t\geq 0. \]
DOI : 10.4064/ba61-2-9
Keywords: prove sums independent random vectors satisfy max leq leq right leq max leq leq quad geq

Zbigniew S. Szewczak 1

1 Faculty of Mathematics and Computer Science Nicolaus Copernicus University 87-100 Toruń, Poland 
@article{10_4064_ba61_2_9,
     author = {Zbigniew S. Szewczak},
     title = {On the {Maximal} {L\'evy{\textendash}Ottaviani} {Inequality} for {Sums} of {Independent} and {Dependent} {Random} {Vectors}},
     journal = {Bulletin of the Polish Academy of Sciences. Mathematics},
     pages = {155--160},
     publisher = {mathdoc},
     volume = {61},
     number = {2},
     year = {2013},
     doi = {10.4064/ba61-2-9},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.4064/ba61-2-9/}
}
TY  - JOUR
AU  - Zbigniew S. Szewczak
TI  - On the Maximal Lévy–Ottaviani Inequality for Sums of Independent and Dependent Random Vectors
JO  - Bulletin of the Polish Academy of Sciences. Mathematics
PY  - 2013
SP  - 155
EP  - 160
VL  - 61
IS  - 2
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/articles/10.4064/ba61-2-9/
DO  - 10.4064/ba61-2-9
LA  - en
ID  - 10_4064_ba61_2_9
ER  - 
%0 Journal Article
%A Zbigniew S. Szewczak
%T On the Maximal Lévy–Ottaviani Inequality for Sums of Independent and Dependent Random Vectors
%J Bulletin of the Polish Academy of Sciences. Mathematics
%D 2013
%P 155-160
%V 61
%N 2
%I mathdoc
%U http://geodesic.mathdoc.fr/articles/10.4064/ba61-2-9/
%R 10.4064/ba61-2-9
%G en
%F 10_4064_ba61_2_9
Zbigniew S. Szewczak. On the Maximal Lévy–Ottaviani Inequality for Sums of Independent and Dependent Random Vectors. Bulletin of the Polish Academy of Sciences. Mathematics, Tome 61 (2013) no. 2, pp. 155-160. doi: 10.4064/ba61-2-9

Cité par Sources :