Geodesic
On Distributions of First Passage Times and Optimal Stopping of AR(1) Sequences
Teoriâ veroâtnostej i ee primeneniâ, Tome 53 (2008) no. 3, pp. 458-471

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Sufficient conditions for the exponential boundedness of first passage times of autoregressive (AR(1)) sequences are derived in this paper. An identity involving the mean of the first passage time is obtained. Further, this identity is used for finding a logarithmic asymptotic of the mean of the first passage time of Gaussian AR(1)-sequences from a strip. Accuracy of the asymptotic approximation is illustrated by Monte Carlo simulations. A corrected approximation is suggested to improve accuracy of the approximation. An explicit formula is derived for the generating function of the first passage time for the case of AR(1)-sequences generated by an innovation with the exponential distribution. The latter formula is used to study an optimal stopping problem.
Keywords: first passage time, autoregressive sequences, exponential boundedness, optimal stopping.
Mots-clés : martingales 
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     title = {On {Distributions} of {First} {Passage} {Times} and {Optimal} {Stopping} of {AR(1)} {Sequences}},
     journal = {Teori\^a vero\^atnostej i ee primeneni\^a},
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     year = {2008},
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     url = {http://geodesic.mathdoc.fr/item/TVP_2008_53_3_a2/}
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A. A. Novikov. On Distributions of First Passage Times and Optimal Stopping of AR(1) Sequences. Teoriâ veroâtnostej i ee primeneniâ, Tome 53 (2008) no. 3, pp. 458-471. http://geodesic.mathdoc.fr/item/TVP_2008_53_3_a2/