Strong limit theorems for weighted sums of negatively associated random variables in nonlinear probability

Yuting Lan; Ning Zhang

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arXiv · 1706.05788

Strong limit theorems for weighted sums of negatively associated random variables in nonlinear probability

Yuting Lan·Ning Zhang

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Abstract

In this paper, based on the initiation of the notion of negatively associated random variables under nonlinear probability, a strong limit theorem for weighted sums of random variables within the same frame is achieved without assumptions of independence and identical distribution, from which the Marcinkiewich-Zygmund type and Kolmogorov type strong laws of large numbers are derived. In addition, as applications of our results, Stranssen type invariance principles of negatively associated random variables and vertically independent random variables are proposed respectively.

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Yuting Lan, Ning Zhang. 2017-06-19. Strong limit theorems for weighted sums of negatively associated random variables in nonlinear probability. https://arxiv.org/abs/1706.05788

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