Limiting diffusion for random walks with drift conditioned to stay positive
1978 ◽
Vol 15
(02)
◽
pp. 280-291
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Keyword(s):
Let {ξ k : k ≧ 1} be a sequence of independent, identically distributed random variables with E{ξ 1} = μ ≠ 0. Form the random walk {S n : n ≧ 0} by setting S 0, S n = ξ 1 + ξ 2 + ··· + ξ n , n ≧ 1. Define the random function Xn by setting where α is a norming constant. Let N denote the hitting time of the set (–∞, 0] by the random walk. The principal result in this paper is to show (under appropriate conditions on the distribution of ξ 1) that the finite-dimensional distributions of Xn , conditioned on n < N < ∞ converge to those of the Brownian excursion process.
1974 ◽
Vol 11
(04)
◽
pp. 742-751
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Keyword(s):
1999 ◽
Vol 36
(1)
◽
pp. 78-85
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1979 ◽
Vol 86
(2)
◽
pp. 301-312
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1984 ◽
Vol 95
(1)
◽
pp. 149-154
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2003 ◽
Vol DMTCS Proceedings vol. AC,...
(Proceedings)
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Keyword(s):