Transition phenomena for ladder epochs of random walks with small negative drift
نویسندگان
چکیده
منابع مشابه
Transition Phenomena for Ladder Epochs of Random Walks with Small Negative Drift
For a family of random walks {S(a)} satisfying ES (a) 1 = −a < 0 we consider ladder epochs τ (a) = min{k ≥ 1 : S (a) k < 0}. We study the asymptotic, as a → 0, behaviour of P(τ (a) > n) in the case when n = n(a) → ∞. As a consequence we obtain also the growth rates of the moments of τ (a).
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Let S0 = 0, {Sn}n≥1 be a random walk generated by a sequence of i.i.d. random variables X1,X2, ... and let τ− := min {n ≥ 1 : Sn ≤ 0} and τ := min {n ≥ 1 : Sn > 0}. Assuming that the distribution of X1 belongs to the domain of attraction of an α-stable law, α 6= 1, we study the asymptotic behavior of P(τ± = n) as n → ∞.
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ژورنال
عنوان ژورنال: Advances in Applied Probability
سال: 2009
ISSN: 0001-8678,1475-6064
DOI: 10.1017/s0001867800003803