Difference between revisions of "Markov chain, non-decomposable"
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| − | A [[Markov chain|Markov chain]] whose transition probabilities | + | {{MSC|60J10|60J27}} |
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| + | [[Category:Markov processes]] | ||
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| + | A [[Markov chain|Markov chain]] whose transition probabilities $P_{ij}(t)$ have the following property: For any states $i$ and $j$ there is a time $t_{ij}$ such that $p_{ij}(t_{ij}) > 0 $. The non-decomposability of a Markov chain is equivalent to non-decomposability of its matrix of transition probabilities $P = \left( {p_{ij}} \right)$ for a discrete-time Markov chain, and of its matrix of transition probability densities $Q = \left( {p'_{ij}(0)} \right)$ for a continuous-time Markov chain. The state space of a non-decomposable Markov chain consists of one class of communicating states (cf. [[Markov chain|Markov chain]]). | ||
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| − | Cf. also [[ | + | Cf. also [[Markov chain]] and [[Markov chain, decomposable]] for references. |
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Latest revision as of 20:22, 29 October 2016
2020 Mathematics Subject Classification: Primary: 60J10 Secondary: 60J27 [MSN][ZBL]
A Markov chain whose transition probabilities $P_{ij}(t)$ have the following property: For any states $i$ and $j$ there is a time $t_{ij}$ such that $p_{ij}(t_{ij}) > 0 $. The non-decomposability of a Markov chain is equivalent to non-decomposability of its matrix of transition probabilities $P = \left( {p_{ij}} \right)$ for a discrete-time Markov chain, and of its matrix of transition probability densities $Q = \left( {p'_{ij}(0)} \right)$ for a continuous-time Markov chain. The state space of a non-decomposable Markov chain consists of one class of communicating states (cf. Markov chain).
Comments
Cf. also Markov chain and Markov chain, decomposable for references.
Markov chain, non-decomposable. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Markov_chain,_non-decomposable&oldid=14296