Asymptotic Distribution for Products of Sums of Linear Processes Under Dependence

Abstract

The products of partial sums of linear processes generated by sequences of positive random variables, which are either linear negative quadrant dependent or linear positive quadrant dependent, is asymptotically lognormal. This extends the earlier work on products of partial sums of random variables.

Keywords:

• Asymptotic distribution
• Linear negative (positive) quadrant dependence
• Products of sums

Mathematics Subject Classification:

• 60F05
• 60F15

Acknowledgment

This article was supported by the Basic Research Foundation of Jilin University (No. 201001002, 201103204), the National Natural Science Foundation of China (Grant No. 11101180), and 985 program of Jilin University.