Some Results on Two - Sided Lil Behavior
نویسندگان
چکیده
nh(n) < ∞, where h is from a suitable subclass of the positive, nondecreasing slowly varying functions. Specializing our result to h(n) = (log logn), where p > 1 and to h(n) = (logn), r > 0, we obtain analogues of the Hartman–Wintner LIL in the infinite variance case. Our proof is based on a general result dealing with LIL behavior of the normalized sums {Sn/cn;n ≥ 1}, where cn is a sufficiently regular normalizing sequence.
منابع مشابه
Small Time Two-Sided LIL Behavior for Lévy Processes at Zero
We wish to characterize when a Lévy process Xt crosses boundaries b(t), in a two-sided sense, for small times t, where b(t) satisfies very mild conditions. An integral test is furnished for computing the value of lim supt→0 |Xt|/b(t) = c. In some cases, we also specify a function b(t) in terms of the Lévy triplet, such that lim supt→0 |Xt|/b(t) = 1.
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