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, e-mail: an@xanum.uam.mx

(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.