A+ CATEGORY SCIENTIFIC UNIT

PDF files of articles are only available for institutions which have paid for the online version upon signing an Institutional User License.

Exact strong laws of large numbers for independent random fields

Volume 66 / 2018

Paweł Kurasiński, Przemysław Matuła, André Adler Bulletin Polish Acad. Sci. Math. 66 (2018), 179-188 MSC: Primary 60F15; Secondary 60G60. DOI: 10.4064/ba8153-9-2018 Published online: 19 October 2018

Abstract

Let $\{ X_{\underline{n}}, \underline{n}\in \mathbb{N}^{d}\}$ be a family of independent random variables with multidimensional indices (a random field) with the same distribution as the r.v. $X.$ A necessary and sufficient condition for the strong law of large numbers in this setting is $\mathbb E \vert X\vert \log _{+}^{d-1}\vert X\vert \lt \infty.$ Our goal is to study the almost sure convergence of normalized or weighted sums in the case when this moment condition is not satisfied.

Authors

  • Paweł KurasińskiInstitute of Mathematics
    Marie Curie-Skłodowska University
    Pl. M. Curie-Skłodowskiej 1
    20-031 Lublin, Poland
    e-mail
  • Przemysław MatułaInstitute of Mathematics
    Marie Curie-Skłodowska University
    Pl. M. Curie-Skłodowskiej 1
    20-031 Lublin, Poland
    e-mail
  • André AdlerDepartment of Mathematics
    Illinois Institute of Technology
    Chicago, IL 60616, U.S.A.
    e-mail

Search for IMPAN publications

Query phrase too short. Type at least 4 characters.

Rewrite code from the image

Reload image

Reload image