AISM 53, 799-809
© 2001 ISM

Uniform asymptotic expansion of likelihood ratio for Markov dependent observations

Andrei Novikov

Departamento de Matemáticas, UAM-Iztapalapa, av. Michoacán y la Purísima s/n, col. Vicentina, 09340 México D. F., Mexico,

(Received February 15, 1999; revised July 24, 2000)

Abstract.    An asymptotic expansion of the logarithm of the likelihood ratio for Markov dependent observation is obtained. A functional limit theorem for the likelihood ratio is proved, which gives a way to study limiting distributions of the likelihood ratio based on stopping times, in particular, that of sequential probability ratio test.

Key words and phrases:    Likelihood ratio, Markov process, asymptotic expansion, functional limit theorem, sequential probability ratio test.

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