On the Maximal Lévy–Ottaviani Inequality for Sums of Independent and Dependent Random Vectors
Volume 61 / 2013
Bulletin Polish Acad. Sci. Math. 61 (2013), 155-160
MSC: Primary 60E15; Secondary 11Y65.
DOI: 10.4064/ba61-2-9
Abstract
We prove that the sums $S_k$ of independent random vectors satisfy \[ P\left(\max_{1\leq k\leq n} \| S_k\| > 3t\right) \leq 2\max_{1\leq k\leq n} P(\|S_k\| > t),\quad t\geq 0. \]
