A Lévy–Ottaviani type inequality for the Bernoulli process on an interval

Witold Bednorz and Rafał Martynek

Statistics & Probability Letters, 2020, vol. 162, issue C

Abstract: In this paper we prove a Lévy–Ottaviani type of property for the Bernoulli process defined on an interval. Namely, we show that under certain conditions on functions (ai)i=1n and for independent Bernoulli random variables (εi)i=1n, P(supt∈[0,1]∑i=1nai(t)εi⩾c) is dominated by CP(∑i=1nai(1)εi⩾1), where c and C are explicit numerical constants independent of n. The result is a partial answer to the conjecture of W. Szatzschneider that the domination holds with c=1 and C=2.

Keywords: Concentration inequalities; Tail comparison; Chaining method (search for similar items in EconPapers)
Date: 2020
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DOI: 10.1016/j.spl.2020.108747

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