2. Consider the Markov jump process with generator matrix 1 0 0 −1 1 1 0 −1 0 0 2 -4 2 1007 0 0 0 0000 0 0 0 1 -2 1 0 0 0 0 0 0 -1 1 0 0 0 0 0 0 0 and let (P(t)) be the associated transition semigroup. Find lim→∞ P(t). [10] Hint: find the communicating classes and their hitting probabilities.

Pls heLP ASAP

The sequence (Xn)n>o is a Markov chain with transition matrix 0 을 0 0 0 3 1 0 0 0 4 4 0 } 0 0 0 1 2 1 1 0 0 3 3 0 } 0 } 0 0 0 0 0 0 0 (a) Draw the transition diagram for (Xn). (b) Determine the communicating classes of the chain, stating whether each class is recurrent or transient. (c) Determine the period of each communicating class.

a)

Determine the classes of the Markov chain and whether they are recurrent.

Determine the classes of the Markov chain and whether they are recurrent.

2. Consider a Markov chain {Xn}n≥o having the following transition diagram: 1/2 1 2 5 1/4 3 4 1/2 1/4 6 7 1/2 For this chain, there are two recurrent classes R₁ = {6,7} and R₂ = {1,2,5}, and one transient class R3 = {3,4}. (a) Find the period of state 3. (b) Find f33 and f22. (c) Starting at state 3, find the probability that the chain is absorbed into R₁. (d) Starting at state 3, find the mean absorbation time, i.e., the expected number of steps that the chain is absorbed into R₁ or R₂. Note: there are missing transition probabilities for this chain, but no impact for your solution.

8. consider the Markov chain given below P || 0 0113 45 120 0 LSLLLLLS 250 0113 12 1 10 5 1 1 3 (a) Use the fundamental matrix method, identify what the matrices Q and R are. Find (I — Q)¯¹R. (b) Use the result from part (a) to find the absorption probabilities fo3, f13, f23, ƒ33, and ƒ43.