Central Limit Theorem Approximations for the Number of Runs in Markov-dependent Multi-type Sequences

Abstract

We consider Markov-dependent multi-type sequences and study various kinds of runs (overlapping, non-overlapping, exact, etc.) by examining additive functionals based on state visits and transitions in an appropriately constructed Markov chain. We establish multivariate Central Limit Theorems for the number of these runs and obtain the covariance matrix of the limiting multivariate normal distribution in closed form using the potential matrix. An application in reliability theory is discussed.

Keywords:

• Central Limit Theorem for Runs
• Markov Chains
• Multi State Trials
• Potential Matrix
• Runs

Mathematics Subject Classification:

• Primary 60E05
• Secondary 60J10