2009
DOI: 10.1137/s0040585x97983730
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On Distributions of First Passage Times and Optimal Stopping of AR(1) Sequences

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Cited by 13 publications
(12 citation statements)
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“…Under these technical assumptions and P (z 0 < 0) > 0, the results of [23] ensure that E{τ } < ∞ and (35) holds.…”
Section: Convergence Speedmentioning
confidence: 99%
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“…Under these technical assumptions and P (z 0 < 0) > 0, the results of [23] ensure that E{τ } < ∞ and (35) holds.…”
Section: Convergence Speedmentioning
confidence: 99%
“…(6)] originally proved in [24, Theorem 3] under slightly stronger assumptions. The results of [23] apply to the problem of the first passage of a given barrier from below, but our problem is that of passing the barrier from above. However, since our barrier is equal to zero, the results of [23] apply to the symmetrical version of our problem with X k replaced by −X k and z k by −z k .…”
Section: Convergence Speedmentioning
confidence: 99%
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“…leading to the following result. For the special case µ = 1, this formula was obtained using differential equations based on the generator in [11,Theorem 3].…”
Section: Theorem 32 It Holds Thatmentioning
confidence: 99%
“…Only very few results are known for this problem. In [3] and [11] the innovations are assumed to be exponentially distributed, and in [5] asymptotic results were given for g(x) = x.…”
mentioning
confidence: 99%