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Sharp sufficient conditions for mean convergence of the maximal partial sums of dependent random variables with general norming sequences
Authors: Lê Văn Thành
6    0
Revista de la Real Academia de Ciencias Exactas, Fisicas y Naturales
: 118     : Paper number 108
: https://link.springer.com/article/10.1007/s13398-023-01540-5
: 1523_2 Sharp sufficient conditions for mean convergence of the.pdf
Publishing year: 1/2024
This paper provides sharp sufficient conditions for mean convergence of the maximal partial sums from triangular arrays of dependent random variables with general norming sequences. As an application, we use this result to give a positive answer to an open question in [Test 32(1):74–106, 2023] concerning mean convergence for the maximal partial sums under regularly varying moment conditions. The techniques developed in the present work also enable us to establish a result on mean convergence for sums of pairwise negatively dependent random variables, which gives an improvement of the main result of Sung [Appl Math Lett 26(1):18–24, 2013] and Ordóñez Cabrera and Volodin [J Math Anal Appl 305(2):644–658, 2005].
Mean convergence, Dependent random variables, Maximal partial sum, Regularly varying moment condition, Regularly varying norming sequence
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