Now assume that you are given an N-state Markov chain, in which each state has bi-directional...

Now assume that you are given an N-state Markov chain, in which each state has bi-directional connections with its two neighboring states (i.e., the neighboring states of S1 are S2 and SN; the neighboring states of S2 are S1 and S3, ..., and the neighboring states of SN−1 are SN−2 and SN ). Identify under what conditions (i.e., what values of N) will this N-state Markov chain have a periodic recurrent class, and justify your answer

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orchestra answered 2 years ago

Consider a Markov chain {Xn|n ≥ 0} with state space S = {0, 1, · ·...

Consider a Markov chain {Xn|n ≥ 0} with state space S = {0, 1, · · · } and transition matrix (pij ) given by pij = 1 2 if j = i − 1 1 2 if j = i + 1, i ≥ 1, and p00 = p01 = 1 2 . Find P{X0 ≤ X1 ≤ · · · ≤ Xn|X0 = i}, i ≥ 0 . Q2. Consider the Markov chain given in Q1. Find P{X1,...

Q1. Let {Xn|n ≥ 0} is a Markov chain with state space S. For i ∈...

Q1. Let {Xn|n ≥ 0} is a Markov chain with state space S. For i ∈ S, define τi = min{n ≥ 0|Xn = i}. Show that τi is a stopping time for each i. Q2. Let τi as in Q1. but for any discrete time stochastic process. Is τi a stopping time? Q3. Let {Xn|n ≥ 0} be a Markov chain and i is a state. Define the random time τ = min{n ≥ 0|Xn+1 = i}. If τ...

Q5. Let {Xn|n ≥ 0} is a Markov chain with state space S = {0, 1,...

Q5. Let {Xn|n ≥ 0} is a Markov chain with state space S = {0, 1, 2, 3}, and transition probability matrix (pij ) given by   2 3 1 3 0 0 1 3 2 3 0 0 0 1 4 1 4 1 2 0 0 1 2 1 2   Determine all recurrent states. 1 2 Q6. Let {Xn|n ≥ 0} is a Markov chain with state space S = {0, 1, 2} and transition...

Let {Xn|n ≥ 0} is a Markov chain with state space S = {0, 1, 2,...

Let {Xn|n ≥ 0} is a Markov chain with state space S = {0, 1, 2, 3}, and transition probability matrix (pij ) given by   2 3 1 3 0 0 1 3 2 3 0 0 0 1 4 1 4 1 2 0 0 1 2 1 2   Determine all recurrent states. Q3. Let {Xn|n ≥ 0} is a Markov chain with state space S = {0, 1, 2} and transition probability matrix (pij...

Q1. Let {Xn|n ≥ 0} is a Markov chain with state space S = {0, 1,...

Q1. Let {Xn|n ≥ 0} is a Markov chain with state space S = {0, 1, 2, 3} and transition probability matrix (pij ). Let τi = min{n ≥ 1 : Xn = i}, i = 0, 1, 2, 3. Define Bij = {Xτj = i}. Is Bij ∈ σ(X0, · · · , Xτj ) ? Q2. Let {Xn|n ≥ 0} is a Markov chain with state space S = {0, 1, 2, 3}, X0 = 0, and transition...

Resolve this in R Consider a Markov chain on {0,1,2, ...} such that from state i,...

Resolve this in R Consider a Markov chain on {0,1,2, ...} such that from state i, the chain goes to i + 1 with probability p, 0 <p <1, and goes to state 0 with probability 1 - p. a) Show that this string is irreducible. b) Calculate P0 (T0 = n), n ≥ 1. c) Show that the chain is recurring.

Prove that for a Markov chain on a finite state space, no states are null recurrent.

Xn is a Markov Chain with state-space E = {0, 1, 2}, and transition matrix 0.4...

Xn is a Markov Chain with state-space E = {0, 1, 2}, and transition matrix 0.4 0.2 0.4 P = 0.6 0.3 0.1 0.5 0.3 0.2 And initial probability vector a = [0.2, 0.3, 0.5] For the Markov Chain with state-space, initial vector, and transition matrix discuss how we would calculate the follow; explain in words how to calculate the question below. a) P(X1 = 0, X2 = 0, X3 = 1, X4 = 2|X0 = 2) b) P(X2 =...

Expected number of time intervals until the Markov Chain below is in state 2 again after...

Expected number of time intervals until the Markov Chain below is in state 2 again after starting in state 2? Matrix: [.4,.2,.4] [.6,0,.4] [.2,.5,.3]

1.14 Let Xn be a Markov chain on state space {1,2,3,4,5} with transition matrix P= 0...

1.14 Let Xn be a Markov chain on state space {1,2,3,4,5} with transition matrix P= 0 1/2 1/2 0 0 0 0 0 1/5 4/5 0 0 0 2/5 3/5 1 0 0 0 0 1/2 0 0 0 1/2 (a) Is this chain irreducible? Is it aperiodic? (b) Find the stationary probability vector.

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