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

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dc.abstract.enIn this paper we prove a Levy-Ottaviani type of property for the Bernoulli process dened on an interval. Namely, we show that under certain conditions on functions (ai)ni =1 and for independent Bernoulli random variables ("i)ni=1, P(supt2[0;1]Pni=1 ai(t)"i > c) is dominated by CP(Pni=1 ai(1)"i > 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.
dc.affiliationUniwersytet Warszawski
dc.contributor.authorMartynek, Rafał
dc.contributor.authorBednorz, Witold
dc.date.accessioned2024-01-24T17:48:44Z
dc.date.available2024-01-24T17:48:44Z
dc.date.issued2020
dc.description.financePublikacja bezkosztowa
dc.description.volume162
dc.identifier.doi10.1016/J.SPL.2020.108747
dc.identifier.issn0167-7152
dc.identifier.urihttps://repozytorium.uw.edu.pl//handle/item/101610
dc.identifier.weblinkhttps://api.elsevier.com/content/article/PII:S016771522030050X?httpAccept=text/xml
dc.languageeng
dc.pbn.affiliationmathemathics
dc.relation.ispartofStatistics and Probability Letters
dc.relation.pages108747
dc.rightsClosedAccess
dc.sciencecloudnosend
dc.titleA Lévy–Ottaviani type inequality for the Bernoulli process on an interval
dc.typeJournalArticle
dspace.entity.typePublication