I am currently studying Markov models from the textbook Introduction to Modeling and Analysis of Stochastic Systems, second edition, by Kulkarni. I have just encountered the concept of periodicity in chapter 2: Definition 2.4. (Periodicity). Let $\{ X_n, n \ge 0 \}$ be an irreducible DTMC on state space $S = \{1, 2, \dots, N […]

Categories

## Markov models and calculating the period of each state

- Post author By Q+A Expert
- Post date March 20, 2020
- No Comments on Markov models and calculating the period of each state

- Tags @p3", 2, 3, 4, 5$ cases, 6$ case, and $p^2_{ii} \not= p^4_{ii} \not= p^6_{ii}$ and $p^2_{ii} > 0, and let $d$ be the largest integer such that $$P(X_n = i \vert X_0 = i) > 0 \Rightarrow n \ \text{is an integer multiple of} \ d \tag{2.48}$, and we want to find the period of each state. We then calculate $P^2, by Kulkarni. I have just encountered the concept of periodicity in chapter 2: Definition 2.4. (Periodicity). Let $\{ X_n, dots, I am currently studying Markov models from the textbook Introduction to Modeling and Analysis of Stochastic Systems, I guess we would have that $d = 2$, n, n \ge 0 \}$ be an irreducible DTMC on state space $S = \{1, or is it aperiodicity? And what specifically is meant by period of each state? I would greatly appreciate it if people would please take the, p^4_{ii} > 0, p^6_{ii} > 0$. What can we conclude here? For the $n = 1, P^6$. It is found that $p_{ii} = p^3_{ii} = p^5_{ii} = 0$, p4, p5, right? But for the $n = 2, right? So is this periodicity, second edition, we would have that $d = 1$