Sequential testing of two hypotheses for a stationary Ornstein--Uhlenbeck process
Teoriâ veroâtnostej i ee primeneniâ, Tome 63 (2018) no. 4, pp. 713-729
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The present paper is concerned with the conditionally extremal settings of
the sequential testing problem of two simple hypotheses about a parameter responsible for the local
return rate of a stationary Ornstein–Uhlenbeck
process to its mean value.
Minimization of the Kullback–Leibler divergence is considered as an optimality test.
An asymptotically optimal scheme is put forward, first, in the case when
the error probabilities of the first and the second kind tend to zero,
and, second, in the case when the tested parameters go off to infinity but the distance between them is fixed.
Keywords:
sequential analysis, hypothesis testing, variational statement, fixed error probability formulation, conditionally extremal settings,
SPRT, stationary Ornstein–Uhlenbeck process.
@article{TVP_2018_63_4_a4,
author = {D. I. Lisovskii and A. N. Shiryaev},
title = {Sequential testing of two hypotheses for a stationary {Ornstein--Uhlenbeck} process},
journal = {Teori\^a vero\^atnostej i ee primeneni\^a},
pages = {713--729},
publisher = {mathdoc},
volume = {63},
number = {4},
year = {2018},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/TVP_2018_63_4_a4/}
}
TY - JOUR AU - D. I. Lisovskii AU - A. N. Shiryaev TI - Sequential testing of two hypotheses for a stationary Ornstein--Uhlenbeck process JO - Teoriâ veroâtnostej i ee primeneniâ PY - 2018 SP - 713 EP - 729 VL - 63 IS - 4 PB - mathdoc UR - http://geodesic.mathdoc.fr/item/TVP_2018_63_4_a4/ LA - ru ID - TVP_2018_63_4_a4 ER -
D. I. Lisovskii; A. N. Shiryaev. Sequential testing of two hypotheses for a stationary Ornstein--Uhlenbeck process. Teoriâ veroâtnostej i ee primeneniâ, Tome 63 (2018) no. 4, pp. 713-729. http://geodesic.mathdoc.fr/item/TVP_2018_63_4_a4/