Strong limit theorems for partial sums of a random sequence
نویسندگان
چکیده
Let {ξj ; j ≥ 1} be a centered strictly stationary random sequence defined by S0 = 0, Sn = ∑n j=1 ξj and σ(n) = √ ES2 n, where σ(t), t > 0, is a nondecreasing continuous regularly varying function. Suppose that there exists n0 ≥ 1 such that, for any n ≥ n0 and 0 ≤ ε < 1, there exist positive constants c1 and c2 such that c1 e−(1+ε)x 2/2 ≤ P { |Sn| σ(n) ≥ x } ≤ c2 e −(1−ε)x2/2, x ≥ 1. Under some additional conditions, we investigate strong limit theorems for increments of partial sum processes of the sequence {ξj ; j ≥ 1}. Mathematics Subject Classification 2000: 60F15, 60G17, 60G60.
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