Weak convergence and first passage times
Keyword(s):
Let Sn, n = 1, 2, ‥, denote the partial sums of i.i.d. random variables with the common distribution function F and positive, finite mean. Let N(c) = min [k; Sk > c‥kp], c ≥ 0, 0 ≤ p < 1. Under the assumption that F belongs to the domain of attraction of a stable law with index α, 1 < α ≤ 2, functional central limit theorems for the first passage time process N(nt), 0 ≤ t ≤ 1, when n → ∞, are derived in the function space D[0,1].
Keyword(s):
Keyword(s):
1989 ◽
Vol 3
(1)
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pp. 77-88
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2020 ◽
Vol 57
(1)
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pp. 221-236
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Keyword(s):
1996 ◽
Vol 33
(02)
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pp. 285-310
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