Local probabilities for random walks with negative drift conditioned to stay nonnegative
نویسندگان
چکیده
منابع مشابه
Local probabilities for random walks with negative drift conditioned to stay nonnegative∗
Let {Sn, n ≥ 0} with S0 = 0 be a random walk with negative drift and let τx = min {k > 0 : Sk < −x} , x ≥ 0. Assuming that the distribution of the i.i.d. increments of the random walk is absolutely continuous with subexponential density we describe the asymptotic behavior, as n→∞, of the probabilities P (τx = n) and P(Sn ∈ [y, y+ ∆), τx > n) for fixed x and various ranges of y. The case of latt...
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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 we study the asymptotic behavior, as n → ∞, of the local probabilities P(τ = n) and the conditional local probabilities P(Sn ∈ [x, x+∆)|τ > ...
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ژورنال
عنوان ژورنال: Electronic Journal of Probability
سال: 2014
ISSN: 1083-6489
DOI: 10.1214/ejp.v19-3426