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Abstract. We
investigate a renewal process N(t) = max{n ≥ 1 : Sn = ∑1nXi ≤ t} for t ≥
0 where X1, X2, ... with P(Xi
≥ 0) = 1 (i = 1, 2, ... ) is a sequence of m-dependent or mixing random variables. We give such a
condition under which N(t) has
finite moment. Strong law of large numbers and central limit theorems for
the function N(t) are
given.
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