Doob's estimate for coherent random variables and maximal operators on trees

• Autorzy: Cichomski Stanisław , Osękowski Adam

Identyfikatory

DOI

10.37190/0208-4147.00132

• Języki publikacji: EN

Abstrakty

EN

Let ξ be an integrable random variable defined on (Ω, F, P). Fix k ∈ Z+ and let {G^j_i }_{1≤i≤n,1≤j≤k} be a reference family of sub-σ-fields of F such that {G^j_i }_1≤i≤n is a filtration for each j ∈ {1, . . . , k}. In this article we explain the underlying connection between the analysis of the maximal functions of the corresponding coherent vector and basic combinatorial properties of the uncentered Hardy-Littlewood maximal operator. Following a classical approach of Grafakos, Kinnunen and Montgomery-Smith, we establish an appropriate version of Doob’s celebrated maximal estimate.

Słowa kluczowe

EN

coherent distribution; maximal operator; martingale; best constants

• Wydawca: Wrocław University of Science and Technology
• Czasopismo: Probability and Mathematical Statistics
• Rocznik: 2023
• Tom: Vol. 43, Fasc. 1
• Strony: 109--119
• Opis fizyczny: Bibliogr. 13 poz.

Twórcy

autor

Cichomski Stanisław

• Faculty of Mathematics University of Warsaw, 02-097 Warszawa, Poland

autor

Osękowski Adam

• Faculty of Mathematics University of Warsaw, 02-097 Warszawa, Poland

Bibliografia

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• [9] L. Grafakos and S. Montgomery-Smith, Best constants for uncentered maximal functions, Bull. London Math. Soc. 29 (1997), 60-64.
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Uwagi

Opracowanie rekordu ze środków MEiN, umowa nr SONP/SP/546092/2022 w ramach programu "Społeczna odpowiedzialność nauki" - moduł: Popularyzacja nauki i promocja sportu (2022-2023).