Lie algebra solution of Lie-Markov model: Application of freshness K-value

Abstract

This study presents the invariant conditions of Lie algebra solution for the Lie Markov model. By integrating Lie algebra theorem and Wei-Norman theorem widely applied in various fields, the Lie algebra structure of Lie Markov model can be determined by symmetry analysis. Unlike the restrictions of past limit convergence theorems, the invariant conditions of Lie algebra solution have consistent formula to solve two basic problems of inhomogeneous Markov process: restrictions of limit convergence theorem, and statistical analysis assumptions and model diagnosis. With the impact of freshness quality management on net profit on sales as an example, inhomogeneous Markov process is employed to describe the relationship between changes in K-value and sales volume to solve the problem of statistical assumptions and model diagnosis in previous logistic regression analysis of freshness in the past. It requires only the Lie algebra solution to calculate net profit on sales, also presents the intuitive results of Lie theory in application.

Keywords:

• Lie-Markov model
• time-inhomogeneous Markov process
• invariant conditions
• freshness quality management

2010 AMS Subject Classifications:

• 60J27