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On the Maximal Lévy-Ottaviani Inequality for Sums of Independent and Dependent Random Vectors

Zbigniew S. Szewczak — 2013

Bulletin of the Polish Academy of Sciences. Mathematics

We prove that the sums $S_{k}$ of independent random vectors satisfy $P (m a x_{1 \leq k \leq n} ∥ S_{k} ∥ > 3 t) \leq 2 m a x_{1 \leq k \leq n} P (∥ S_{k} ∥ > t)$ , t ≥ 0.

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