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,
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.

**Source**
(TeX , DVI )