Strong laws of large numbers for the sequence of the maximum of partial sums of i.i.d. random variables

• Autorzy: Chang Shuhua , Li Deli , Rosalsky Andrew

Identyfikatory

DOI

10.19195/0208-4147.39.1.2

• Języki publikacji: EN

Abstrakty

EN

Let 0 < p ≤ 2, let {X_n; n ≥ 1} be a sequence of independent copies of a real-valued random variable X, and set S_n = X₁ + … + X_n, n ≥ 1. Motivated by a theorem of Mikosch (1984), this note is devoted to establishing a strong law of large numbers for the sequence {max_{1 ≤ k ≤ n} |S_k|; n ≥ 1}. More specifically, necessary and sufficient conditions are given for [wzór] a.s., where log x = log_e max{e, x}, x ≥ 0.

Słowa kluczowe

EN

theorem of Mikosch; i.i.d. real-valued random variables; maximum of partial sums; strong law of large numbers

• Wydawca: Wrocław University of Science and Technology
• Czasopismo: Probability and Mathematical Statistics
• Rocznik: 2019
• Tom: Vol. 39, Fasc. 1
• Strony: 19--38
• Opis fizyczny: Bibliogr. 11 poz.

Twórcy

autor

Chang Shuhua

• Tianjin University of Finance and Economics, Research Center for Mathematics and Economics, Tianjin 300222, China

autor

Li Deli

• Lakehead University, Department of Mathematical Sciences, Thunder Bay, ON P7B 5E1, Canada

autor

Rosalsky Andrew

• University of Florida, Department of Statistics, Gainesville, Florida 32611, USA

Bibliografia

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