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I'm just wondering what the difference between stationary probability and limiting probability is.

And, if any of you know: What does it mean that some elements exist and some elements doesn't, when $\lim_{k \to \infty} \mathbf{P}^{(k)}$. Here, $\mathbf{P}$ is transition probability matrix describing a descrete-time Markov chain.

I'd really appreciate some advice!

truglr
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    You should look at this answer. – Ritz Oct 07 '14 at 07:37
  • Thank you, @Ritz! I actually saw the question before I asked mine, since I thought stationary and limiting probabilities were a bit different than stationary and limiting distributions, but now I guess they're not :) – truglr Oct 07 '14 at 07:50
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    Let's say the state space of our Markov chain is $S$. Then, $p(i), ~ i \in S$ is a specific stationary probability and $p(\cdot)$ (so for all states in $S$) is the stationary distribution. In essence the distribution describes all stationary probabilities. Hope this clarifies it for you. – Ritz Oct 07 '14 at 08:05
  • Ah, that clarifies it! Thank you so much. – truglr Oct 07 '14 at 08:13

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