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

Shang Yilun (Institute for Cyber Security, University of Texas at San Antonio, Texas , USA)

In this note, we prove a central limit theorem for the sum of a random number Nn of m-dependent random variables. The sequence Nn and the terms in the sum are not assumed to be independent. Moreover, the conditions of the theorem are not stringent in the sense that a simple moving average sequence serves as an example.

Keywords: Central limit theorem, dependent random variables, stationary sequence