TY - JOUR
T1 - Asymptotic exponentiality of the distribution of first exit times for a class of markov processes with applications to quickest change detection?
AU - Pollak, M.
AU - Tartakovsky, A. G.
PY - 2009
Y1 - 2009
N2 - We consider the first exit time of a nonnegative Harris-recurrent Markov process from the interval [0, A] as A ? ?. We provide an alternative method of proof of asymptotic exponentiality of the first exit time (suitably standardized) that does not rely on embedding in a regeneration process. We show that under certain conditions the moment generating function of a suitably standardized version of the first exit time converges to that of Exponential(1), and we connect between the standardizing constant and the quasi-stationary distribution (assuming it exists). The results are applied to the evaluation of a distribution of run length to false alarm in change-point detection problems.
AB - We consider the first exit time of a nonnegative Harris-recurrent Markov process from the interval [0, A] as A ? ?. We provide an alternative method of proof of asymptotic exponentiality of the first exit time (suitably standardized) that does not rely on embedding in a regeneration process. We show that under certain conditions the moment generating function of a suitably standardized version of the first exit time converges to that of Exponential(1), and we connect between the standardizing constant and the quasi-stationary distribution (assuming it exists). The results are applied to the evaluation of a distribution of run length to false alarm in change-point detection problems.
KW - Asymptotic exponentiality
KW - Change-point problems
KW - Cusum procedures
KW - First exit time
KW - Shiryaev-roberts procedures
UR - http://www.scopus.com/inward/record.url?scp=69549091635&partnerID=8YFLogxK
U2 - 10.1137/S0040585X97983742
DO - 10.1137/S0040585X97983742
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AN - SCOPUS:69549091635
SN - 0040-585X
VL - 53
SP - 430
EP - 442
JO - Theory of Probability and its Applications
JF - Theory of Probability and its Applications
IS - 3
ER -