Geodesic
On asymptotical optimality of criterion in a~hypothesis testing problem for Markov jump processes
Zapiski Nauchnykh Seminarov POMI, Boundary-value problems of mathematical physics and related problems of function theory. Part 18, Tome 153 (1986), pp. 105-114

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A family of jumping Markov processes depending on a real parameter is considered. We test a simple hypothesis versus one-sided alternative on the base of increasing volume of observations. We suggest a test for this problem which is proved to be second order asymptotically efficient. This proof does not require asymptotic expansions of power functions. 
@article{ZNSL_1986_153_a8,
     author = {V. K. Malinovskii},
     title = {On asymptotical optimality of criterion in a~hypothesis testing problem for {Markov} jump processes},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {105--114},
     publisher = {mathdoc},
     volume = {153},
     year = {1986},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_1986_153_a8/}
}
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%J Zapiski Nauchnykh Seminarov POMI
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%I mathdoc
%U http://geodesic.mathdoc.fr/item/ZNSL_1986_153_a8/
%G ru
%F ZNSL_1986_153_a8
V. K. Malinovskii. On asymptotical optimality of criterion in a~hypothesis testing problem for Markov jump processes. Zapiski Nauchnykh Seminarov POMI, Boundary-value problems of mathematical physics and related problems of function theory. Part 18, Tome 153 (1986), pp. 105-114. http://geodesic.mathdoc.fr/item/ZNSL_1986_153_a8/