Local probabilities for random walks with negative drift conditioned to stay nonnegative∗
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چکیده
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 lattice distribution of increments is considered as well.
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تاریخ انتشار 2014