Question

How to show persistence of a three-state Markov-chain $P =\left(\begin{smallmatrix}p&1-p&0\\0&0&1\\1-q&q&0\end{smallmatrix}\right)$?

score 221 · Answer 1 · 2026-04-14 18:39:09

221

Views

How to show persistence of a three-state Markov-chain $P =\left(\begin{smallmatrix}p&1-p&0\\0&0&1\\1-q&q&0\end{smallmatrix}\right)$?

Published on 14 Apr 2026 - 18:39

score 191 · Answer 2 · 2026-04-16 04:06:56

191

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Show $1$ is a persistent null state in $\left(\begin{smallmatrix}1/2&1/2&0\\0&0&1\\\frac{1}{n+1}&0 &\frac{n}{n+1}\end{smallmatrix}\right)$

Published on 16 Apr 2026 - 4:06

score 230 · Answer 3 · 2026-04-12 09:23:40

230

Views

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score 73 · Answer 4 · 2026-04-10 10:47:40

73

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504

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score 84 · Answer 6 · 2026-03-26 06:22:28

84

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score 105 · Answer 7 · 2026-04-15 00:55:26

105

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score 159 · Answer 8 · 2026-04-10 02:07:58

159

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score 34 · Answer 9 · 2026-04-17 12:44:43

34

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score 484 · Answer 10 · 2026-04-11 12:48:18

484

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648

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score 146 · Answer 12 · 2026-04-17 07:55:15

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score 63 · Answer 13 · 2026-04-09 11:59:06

63

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score 42 · Answer 14 · 2026-04-17 12:40:39

42

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score 145 · Answer 15 · 2026-04-15 10:34:40

145

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Published on 15 Apr 2026 - 10:34

List Question

How to show persistence of a three-state Markov-chain $P =\left(\begin{smallmatrix}p&1-p&0\\0&0&1\\1-q&q&0\end{smallmatrix}\right)$?

Show $1$ is a persistent null state in $\left(\begin{smallmatrix}1/2&1/2&0\\0&0&1\\\frac{1}{n+1}&0 &\frac{n}{n+1}\end{smallmatrix}\right)$

Given the infinitesimal generator, how a continuous Markov chain behaves after the exploding time?

Need help with a Homogeneous Poisson Process Question

Continuous Time Markov Chain Question

Probability of failure at year i vs Probability of failure up to year i

Counter example regarding the covariance matrix of a stationary process $\{X_{t}\}$

How to recover the continuous Markov chain from its infinitesimal generator?

Why $\mathbb E[\Phi(X,Y)]=\int\mathbb E[\Phi(x,Y)]\mathbb P\{X\in dx\}=\mathbb E\int \Phi(x,Y)\mathbb P\{X\in dx\}$ is a consequence of this lemma?

Exponential distribution and Markov chain problem

Absolute value of a symmetric 'simple' random walk

Find $\text{Cov}(N_{1}(t),N_{2}(t))$

Equivalent conditions for local martingales

What does it mean by "the process starts out in state $i$"?

Leveraging pure math knowledge to learn applied math

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