Nearly completely decomposable Markov chain
In probability theory, a nearly completely decomposable Markov chain is a Markov chain where the state-space can be partitioned in such a way that movement within a partition occurs much more frequently that movement between partitions.[1] Particularly efficient algorithms exist to compute the stationary distribution of Markov chains with this property.[2]
Definition
Ando and Fisher define a completely decomposable matrix as one where "an identical rearrangement of rows and columns leaves a set of square submatrixes on the pricnipal diagonal and zeros everywhere else." A nearly completely decomposable matrix is one where "zeroes everywhere else" is replaced with "small nonzeros everywhere else."[3][4]
See also
References
- ^ Attention: This template ({{cite jstor}}) is deprecated. To cite the publication identified by jstor:1427937, please use {{cite journal}} with
|jstor=1427937instead. - ^ Attention: This template ({{cite doi}}) is deprecated. To cite the publication identified by doi:10.1137/0605019, please use {{cite journal}} (if it was published in a bona fide academic journal, otherwise {{cite report}} with
|doi=10.1137/0605019instead. - ^ Attention: This template ({{cite doi}}) is deprecated. To cite the publication identified by doi:10.2307.2F2525455, please use {{cite journal}} (if it was published in a bona fide academic journal, otherwise {{cite report}} with
|doi=10.2307.2F2525455instead. - ^ Attention: This template ({{cite jstor}}) is deprecated. To cite the publication identified by jstor:1913078, please use {{cite journal}} with
|jstor=1913078instead.