Probability and Measure

Asymptotic results for random sums of dependent random variables

Classical central limit theorem is considered the heart of probability and statistics theory. Our interest in this paper is central limit theorems for functions of random variables under mixing conditions. We impose mixing conditions on the differences between the joint cumulative distribution functions and the product of the marginal cumulative distribution functions. By using characteristic functions, we obtain several limit theorems extending previous results.

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A Note on the Central Limit Theorems for Dependent Random Variables

Random central limit theorem for associated random variables and the order of approximation

Normal approximation for strong demimartingales

Inthisnote,weproveacentrallimittheoremforthesumofarandomnumberNn ofm-dependent randomvariables. ThesequenceNn andthetermsinthesumarenotassumedtobeindependent. Moreover, the conditions of the theorem are not stringent in the sense that a simple moving average sequence serves as an example.

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Yilun Shang

Papers

A central limit theorem for randomly indexed m-dependent random variables