A class of strong deviation theorems for the sequence of real valued random variables with respect to continuous-state non-homogeneous Markov chains

Abstract

In this paper, we consider the asymptotic behavior of the log-likelihood ratio as a measure of the deviation between a sequence of real valued random variables and a continuous-state non-homogeneous Markov chains. Then, by using the supermartingale limit theorem, we establish a class of strong deviation theorems for bivariate functions of the sequence of real valued random variables which are associated with the continuous-state non-homogeneous Markov chains.

Keywords:

• Sequence of real valued random variables
• log-likelihood ratio
• strong deviation theorem
• continuous-state non-homogeneous Markov chains

MSC(2000):

• 60F15
• 60J10

Acknowledgements

The authors are very thankful to the reviewers for their detail valuable comments which make the paper great improvement both in mathematics and English.

Additional information

Funding

This work is supported by the National Natural Science Foundation of China (11571142, 11601191), Youth talent cultivation project of Jiangsu University, Young science and technology talents lifting project of Jiangsu association for science and technology.