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

Volume 61 / 2013

Zbigniew S. Szewczak 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 \[ P\left(\max_{1\leq k\leq n} \| S_k\| > 3t\right) \leq 2\max_{1\leq k\leq n} P(\|S_k\| > t),\quad t\geq 0. \]

Authors

  • Zbigniew S. SzewczakFaculty of Mathematics and Computer Science
    Nicolaus Copernicus University
    87-100 Toruń, Poland
    e-mail

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