Strong law of large numbers for random variables with multidimensional indices

• Autorzy: Gdula A. M. , Krajka A.

Identyfikatory

DOI

10.19195/0208-4147.37.1.8

• Języki publikacji: EN

Abstrakty

EN

Let {X_n, n ϵ V ⸦ N²} be a two-dimensional random field of independent identically distributed random variables indexed by some subset V of lattice N². For some sets V the strong law of large numbers [wzór] is equivalent to EX₁ = μ and [wzór]. In this paper we characterize such sets V.

Słowa kluczowe

EN

strong law of large numbers; sums of random fields; multidimensional index

• Wydawca: Wrocław University of Science and Technology
• Czasopismo: Probability and Mathematical Statistics
• Rocznik: 2017
• Tom: Vol. 37, Fasc. 1
• Strony: 185--199
• Opis fizyczny: Bibliogr. 10 poz., wykr.

Twórcy

autor

Gdula A. M.

• Institute of Mathematics, Maria Curie-Skłodowska University, pl. Marii Curie-Skłodowskiej 1, 20-031 Lublin, Poland

autor

Krajka A.

• Institute of Computer Sciences, Maria Curie-Skłodowska University, pl. Marii Curie-Skłodowskiej 1, 20-031 Lublin, Poland

Bibliografia

• [1] N. Dunford, An individual ergodic theorem for noncommutative transformations, Acta Sci. Math. (Szeged) 14 (1951), pp. 1-4.
• [2] J.-P. Gabriel, Martingales with a countable filtering index set, Ann. Probab. 5 (1977), pp. 888-898.
• [3] A. Gut, Strong laws for independent identically distributed random variables indexed by a sector, Ann. Probab. 11 (3) (1983), pp. 569-577.
• [4] K.-H. Indlekofer and I. O. Klesov, Strong law of large numbers for multiple sums whose indices belong to a sector with function boundaries, Theory Probab. Appl. 52 (4) (2008), pp. 711-719.
• [5] I. O. Klesov, Strong law of large numbers for multiple sums of independent identically distributed random variables (in Russian), Mat. Zametki 38 (6) (1985), pp. 915-930.
• [6] I. O. Klesov and Z. Rychlik, Strong laws of large numbers on partially ordered sets, Theory Probab. Math. Statist. 58 (1999), pp. 35-41.
• [7] R. T. Smythe, Strong laws of large numbers for r-dimensional arrays of random variables, Ann. Probab. 1 (1973), pp. 164-170.
• [8] R. T. Smythe, Sums of independent random variables on partially ordered sets, Ann. Probab. 2 (1974), pp. 906-917.
• [9] N. Wiener, The ergodic theorem, Duke Math. J. 5 (1939), pp. 1-18.
• [10] A. Zygmund, An individual ergodic theorem for noncommutative transformations, Acta Sci. Math. (Szeged) 14 (1951), pp. 103-110.

Uwagi

Opracowanie rekordu w ramach umowy 509/P-DUN/2018 ze środków MNiSW przeznaczonych na działalność upowszechniającą naukę (2019).