On a contraction property of Bernoulli canonical processes

• Autorzy: Bednorz Witold , Martynek Rafał

Identyfikatory

DOI

10.4064/ba8111-4-2019

• Języki publikacji: EN

Abstrakty

EN

We give several results concerning suprema of canonical processes. The main theorem concerns a contraction property of Bernoulli canonical processes which generalizes the one proved by Talagrand (1993). It states that for independent Rademacher random variables (ε_i)_i≥1 we can compare E sup_tϵT Σ_i≥1 φ_i(t) ε_i with E sup_tϵT Σ_i=1^∞ t_i ε_i, where the function φ = (φ_i)_i≥1: T → l², T ⊂ l², satisfies certain conditions. Originally, it was assumed that each φ_i is a contraction. We relax this assumption to comparability of Gaussian parts of increments: for all s, t ϵ T and p ≥ 0, [formula], where C ≥ 1 is an absolute constant and I ⊂ N, I^c = N \ I.

Słowa kluczowe

EN

Bernoulli process; Bernoulli comparison; canonical processes; chaining methods; weak moments; strong moments

• Wydawca: Instytut Matematyczny PAN
• Czasopismo: Bulletin of the Polish Academy of Sciences. Mathematics
• Rocznik: 2019
• Tom: Vol. 67, no. 2
• Strony: 187--209
• Opis fizyczny: Bibliogr. 19 poz.

Twórcy

autor

Bednorz Witold

• Institute of Mathematics, University of Warsaw, Banacha 2, 02-097 Warszawa, Poland

autor

Martynek Rafał

• Institute of Mathematics, University of Warsaw, Banacha 2, 02-097 Warszawa, Poland

Bibliografia

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Uwagi

Opracowanie rekordu ze środków MNiSW, umowa Nr 461252 w ramach programu "Społeczna odpowiedzialność nauki" - moduł: Popularyzacja nauki i promocja sportu (2020).