On a new concept of stochastic domination and the laws of large numbers
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Lê Vǎn Thành [1]
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[1] Vinh University
Vinh University
Vietnam
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- Localización: Test: An Official Journal of the Spanish Society of Statistics and Operations Research, ISSN-e 1863-8260, ISSN 1133-0686, Vol. 32, Nº. 1, 2023, págs. 74-106
- Idioma: inglés
- Texto completo no disponible (Saber más ...)
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Resumen
Consider a sequence of positive integers {kn,n≥1}, and an array of nonnegative real numbers {an,i,1≤i≤kn,n≥1} satisfying supn≥1∑kni=1an,i=C0∈(0,∞). This paper introduces the concept of {an,i}-stochastic domination. We develop some techniques concerning this concept and apply them to remove an assumption in a strong law of large numbers of Chandra and Ghosal (Acta Math Hung 71(4):327–336, 1996). As a by-product, a considerable extension of a recent result of Boukhari (J Theor Probab, 2021. https://doi.org/10.1007/s10959-021-01120-6) is established and proved by a different method. The results on laws of large numbers are new even when the summands are independent. Relationships between the concept of {an,i}-stochastic domination and the concept of {an,i}-uniform integrability are presented. Two open problems are also discussed.
