Abstract
We give here an almost sure central limit theorem for product of sums of strongly mixing positive random variables.
Highlights
Introduction and ResultsThere has been a lot of work on the almost sure central limit theorem ASCLT , we can refer to Brosamler 1 , Schatte 2 , Lacey and Philipp 3 , and Peligrad and Shao 4
Introduction and ResultsIn recent decades, there has been a lot of work on the almost sure central limit theorem ASCLT, we can refer to Brosamler 1, Schatte 2, Lacey and Philipp 3, and Peligrad and Shao 4 .Khurelbaatar and Rempala 5 gave an ASCLT for product of partial sums of i.i.d. random variables as follows.Theorem 1.1
There has been a lot of work on the almost sure central limit theorem ASCLT, we can refer to Brosamler 1, Schatte 2, Lacey and Philipp 3, and Peligrad and Shao 4
Summary
There has been a lot of work on the almost sure central limit theorem ASCLT , we can refer to Brosamler 1 , Schatte 2 , Lacey and Philipp 3 , and Peligrad and Shao 4. Khurelbaatar and Rempala 5 gave an ASCLT for product of partial sums of i.i.d. random variables as follows. Let {Xn, n ≥ 1} be a sequence of i.i.d. positive random variables with EX1 and Var X1 σ2. Jin 6 had proved that 1.1 holds under appropriate conditions for strongly mixing positive random variables and gave an ASCLT for product of partial sums of strongly mixing as follows. Let {Xn, n ≥ 1} be a sequence of identically distributed positive strongly mixing random variable with EX1 μ > 0 and Var X1 σ2, dk 1/k, Dn n k
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