Effect of Dependence on the Occupation Time in a Two-State Stationary Markov Chain

Abstract

The occupation time X_n of a Markov chain is the time spent in a given state up to the time t = n. For a two-state stationary Markov chain, the behavior of X_n depends on the two parameters p, the proportion of time in state 1, and d, the dependence parameter. We generate a set of tables for the tail probabilities Pr[X_n ≤ x] and show that they are not necessarily monotone functions of d. Errors in hypothesis tests for p based on the binomial variable do not necessarily increase with increasing d, and confidence limits for p need not necessarily be monotone.

Key Words:

• Dependence
• Occupation time
• Markov chain