Question

Let (pij ) be a stochastic matrix and {Xn|n ≥ 0} be an S-valued stochastic process...

Let (pij ) be a stochastic matrix and {Xn|n ≥ 0} be an S-valued stochastic process with finite dimensional distributions given by P(X0 = i0, X1 = i1, · · · , Xn = in) = P(X0 = i0)pi0i1 · · · pin−1in , n ≥ 0, i0, · · · , in ∈ S. Then {Xn|n ≥ 0} is a Markov chain with transition probability matrix (pij ).

Let {Xn|n ≥ 0} be an S-valued Markov chain. Then the finite dimensional distributions are given as follows. For i0, · · · , in ∈ S, n ≥ 0 (0.2) P(X0 = i0, · · · , Xn = in) = P(X0 = i0)P(X1 = i1|X0 = i0)· · · P(Xn = in|Xn−1 = in−1).

Math   Statistics-And-Probability   
0 0
Add a commentTranscribed image text
Next >

Homework Answers

Answer #1

0 0
Know the answer?
Your Answer:

Post as a guest

Your Name:

What's your source?

Earn Coins

Coins can be redeemed for fabulous gifts.

Log In

Sign Up

Not the answer you're looking for?
Ask your own homework help question
Similar Questions
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}, X0 = 0, 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   Let τ0 = min{n ≥ 1 : Xn = 0} and B = {Xτ0 = 0}. Compute P(Xτ0+2 = 2|B). . Classify all...
1. Consider the Markov chain {Xn|n ≥ 0} associated with Gambler’s ruin with m = 3....
1. Consider the Markov chain {Xn|n ≥ 0} associated with Gambler’s ruin with m = 3. Find the probability of ruin given X0 = i ∈ {0, 1, 2, 3} 2 Let {Xn|n ≥ 0} be a simple random walk on an undirected graph (V, E) where V = {1, 2, 3, 4, 5, 6, 7} and E = {{1, 2}, {1, 3}, {1, 6}, {2, 4}, {4, 6}, {3, 5}, {5, 7}}. Let X0 ∼ µ0 where µ0({i}) =...
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     ? P = 0.6 0.3    ? 0.5 0.3    ? And initial probability vector a = [0.2, 0.3, ?] a) What are the missing values (?) in the transition matrix an initial vector? b) P(X1 = 0) = c) P(X1 = 0|X0 = 2) = d) P(X22 = 1|X20 = 2) = e) E[X0] = For the Markov Chain with state-space, initial vector, and...
The transition probability matrix of a Markov chain {Xn }, n = 1,2,3……. having 3 states...
The transition probability matrix of a Markov chain {Xn }, n = 1,2,3……. having 3 states 1, 2, 3 is P = 0.1 0.5 0.4 0.6 0.2 0.2 0.3 0.4 0.3 * and the initial distribution is P(0) = (0.7, 0.2,0.1) Find: i. P { X3 =2, X2 =3, X1 = 3, X0 = 2} ii. P { X3 =3, X2 =1, X1 = 2, X0 = 1} iii. P{X2 = 3}
asasap Consider the Markov chain with state space {1, 2, 3} and transition matrix  ...
asasap Consider the Markov chain with state space {1, 2, 3} and transition matrix   1 2 1 4 1 4 0 1 0 1 4 0 3 4   Find the periodicity of the states. \ Let {Xn|n ≥ 0} be a finite state Markov chain. prove or disprove that all states are positive recurren
A Markov chain X0, X1, ... on states 0, 1, 2 has the transition probability matrix...
A Markov chain X0, X1, ... on states 0, 1, 2 has the transition probability matrix P = {0.1 0.2 0.7        0.9 0.1   0        0.1 0.8 0.1} and initial distribution p0 = Pr{X0 = 0} = 0.3, p1 = Pr{X0 = 1} = 0.4, and p2 = Pr{X0 = 2} = 0.3. Determine Pr{X0 = 0, X1 = 1, X2 = 2}. Please tell me what it means of the initial distribution why initial distribution p0 = Pr{X0...
Consider the state space {rain, no rain} to describe the weather each day. Let {Xn} be...
Consider the state space {rain, no rain} to describe the weather each day. Let {Xn} be the stochastic process with this state space describing the weather on the nth day. Suppose the weather obeys the following rules: – If it has rained for two days straight, there is a 20% chance that the next day will be rainy. – If today is rainy but yesterday was not, there is a 50% chance that tomorrow will be rainy. – If yesterday...
Consider a Markov chain {Xn; n = 0, 1, 2, . . . } on S...
Consider a Markov chain {Xn; n = 0, 1, 2, . . . } on S = N = {0, 1, 2, . . . } with transition probabilities P(x, 0) = 1/2 , P(x, x + 1) = 1/2 ∀x ∈ S, . (a) Show that the chain is irreducible. (b) Find P0(T0 = n) for each n = 1, 2, . . . . (c) Use part (b) to show that state 0 is recurrent; i.e., ρ00 =...
Let n ≥ 2 and x1, x2, ..., xn > 0 be such that x1 +...
Let n ≥ 2 and x1, x2, ..., xn > 0 be such that x1 + x2 + · · · + xn = 1. Prove that √ x1 + √ x2 + · · · + √ xn /√ n − 1 ≤ x1/ √ 1 − x1 + x2/ √ 1 − x2 + · · · + xn/ √ 1 − xn
Suppose that a production process changes states according to a Markov process whose one-step probability transition...
Suppose that a production process changes states according to a Markov process whose one-step probability transition matrix is given by 0 1 2 3 0 0.3 0.5 0 0.2 1 0.5 0.2 0.2 0.1 2 0.2 0.3 0.4 0.1 3 0.1 0.2 0.4 0.3 a. What is the probability that the process will be at state 2 after the 105th transition given that it is at state 0 after the 102 nd transition? b. What is the probability that the...
ADVERTISEMENT
Need Online Homework Help?

Get Answers For Free
Most questions answered within 1 hours.

Ask a Question
ADVERTISEMENT