On normal approximation of discounted and strongly mixing random variables |
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Authors: | J Sunklodas |
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Institution: | (1) Institute of Mathematics and Informatics, Akademijos 4, LT-08663 Vilnius;(2) Vilnius Gediminas Technical University, Saulétekio 11, LT-10223 Vilnius, Lithuania |
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Abstract: | We estimate the difference
for bounded functions h: ℝ → ℝ satisfying the Lipschitz condition, where Z
v
= B
v
−1
∑
i=0
∞
v
i
X
i
and
with discount factor ν such that 0 < ν < 1. Here {X
n
, n ≥ 0} is a sequence of strongly mixing random variables with
, and N is a standard normal random variable. In a particular case, the obtained upper bounds are of order O((1 − ν)1/2).
Published in Lietuvos Matematikos Rinkinys, Vol. 47, No. 3, pp. 399–409, July–September, 2007.
The research was partially supported by the Lithuanian State Science and Studies Foundation, grant No. T-15/07. |
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Keywords: | discounted central limit theorem strong mixing condition Lipschitz condition Stein’ s method |
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