A remark on the exact laws of large numbers for ratios of independent random variables

• Autorzy: Matuła Przemysław

Identyfikatory

DOI

10.37190/0208-4147.00071

• Języki publikacji: EN

Abstrakty

EN

Let (X_n)_n∈N and (Y_n)_n∈N be two sequences of i.i.d. random variable ξ which are independent of each other and all have the distribution of a positive random variable ξ with density f_ξ . We study weighted strong laws of large numbers for the ratios of the form [wzór]1 in the cases when IEξ = ∞ or lim_x→0+ f_ξ (x) = 0 or f_ξ is unbounded. This research complements some results known so far.

Słowa kluczowe

EN

almost sure convergence; law of large numbers; i.i.d. random variables

• Wydawca: Wrocław University of Science and Technology
• Czasopismo: Probability and Mathematical Statistics
• Rocznik: 2022
• Tom: Vol. 42, Fasc. 2
• Strony: 219--225
• Opis fizyczny: Bibliogr. 6 poz.

Twórcy

autor

Matuła Przemysław

• Institute of Mathematics Marie Curie-Skłodowska University, Pl. M. Curie-Skłodowskiej 1, 20-031 Lublin, Poland

Bibliografia

• [1] A. Adler, Exact strong laws, Bull. Inst. Math. Acad. Sinica 28 (2000), 141-166.
• [2] A. Adler, Laws of large numbers for ratios of uniform random variables, Open Math. 13 (2015), 571-576.
• [3] P. Kurasiński and P. Matuła, Exact weak laws of large numbers with applications to ratios of random variables, Appl. Math. (Warsaw) 47 (2020), 59-66.
• [4] P. Kurasiński, Exact laws of large numbers with applications, PhD thesis, 2022.
• [5] P. Matuła, A. Adler and P. Kurasi ́nski, On exact strong laws of large numbers for ratios of random variables and their applications, Comm. Statist. Theory Methods 49 (2020), 3153-3167.
• [6] P. Matuła, P. Kurasi ́nski and A. Adler, Exact strong laws of large numbers for ratios of the smallest order statistics, Statist. Probab. Lett. 152 (2019), 69-73.