A large deviation local limit theorem
1989 ◽
Vol 105
(3)
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pp. 575-577
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The following elegant one-sided large deviation result is given by S. V. Nagaev in [2].Theorem 0. Suppose that {Sn,n ≤ 0} is a random walk whose increments Xi are independent copies of X, where(X) = 0 andPr{X > x} ̃ x−αL(x) as x→ + ∞,and where 1 < α < ∞ and L is slowly varying at ∞. Then for any ε > 0 and uniformly in x ≥ εnPr{Sn > x} ̃ n Pr{X > x} as n→∞.It is the purpose of this note to point out that for lattice-valued random walks there is an analogous local limit theorem.
2008 ◽
Vol 11
(02)
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pp. 213-229
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2018 ◽
Vol 371
(4)
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pp. 2553-2573
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2002 ◽
Vol 73
(3)
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pp. 301-334
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2002 ◽
Vol 56
(4)
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pp. 399-404
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2010 ◽
Vol 152
(3-4)
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pp. 407-424
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2018 ◽
Vol 128
(12)
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pp. 4000-4017
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2017 ◽
Vol 127
(4)
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pp. 1282-1296
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