A strong approximation for logarithmic averages of partial sums of random variables |
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Authors: | G Hurelbaatar |
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Institution: | (1) Mathematical Institute of the, Hungarian Academy of Sciences, P.O. Box 127, H-1364 Budapest, Hungary |
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Abstract: | LetS
n be the partial sums of -mixing stationary random variables and letf(x) be a real function. In this note we give sufficient conditions under which the logarithmic average off(S
n
/
n
) converges almost surely to
–
f(x)d(x). We also obtain strong approximation forH(n)=
k=1
n
k
–1
f(S
k
/k)=logn
–
f(x)d(x) which will imply the asymptotic normality ofH(n)/log1/2
n. But for partial sums of i.i.d. random variables our results will be proved under weaker moment condition than assumed for -mixing random variables. |
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Keywords: | Primary 60F15 60F05 |
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