Markov transition matrix in canonical form?

[cdotter]

As I understand, a Markov chain transition matrix rewritten in its canonical form is a large matrix that can be separated into quadrants: a zero matrix, an identity matrix, a transient to absorbing matrix, and a transient to transient matrix.

The zero matrix and identity matrix parts are easy enough, but I have no idea how to write transient to absorbing or transient to transient matrix. I've also found other sources that tell me to "rewrite the transition matrix so the transient states come first." I have no idea what this means.

I have also found an example, the drunken something or other problem, but the transition matrix is already written in its canonical form. This doesn't help me at all.

Could someone give me a dumbed down step-by-step guide, or maybe a worked example?

 

[Ray Vickson]

As I understand, a Markov chain transition matrix rewritten in its canonical form is a large matrix that can be separated into quadrants: a zero matrix, an identity matrix, a transient to absorbing matrix, and a transient to transient matrix.

The zero matrix and identity matrix parts are easy enough, but I have no idea how to write transient to absorbing or transient to transient matrix. I've also found other sources that tell me to "rewrite the transition matrix so the transient states come first." I have no idea what this means.

I have also found an example, the drunken something or other problem, but the transition matrix is already written in its canonical form. This doesn't help me at all.

Could someone give me a dumbed down step-by-step guide, or maybe a worked example?

Your understanding seems faulty; there are many transition matrices that do not fit the pattern you describe. Why not read some standard sources, such as: http://www.cs.virginia.edu/~gfx/courses/2006/DataDriven/bib/texsyn/Chapter11.pdf ? This has numerous examples and has most of what you say you want.

RGV

 

[cdotter]

Nevermind, I figured it out. :)

http://www.aw-bc.com/greenwell/markov.pdf Example 7

 

[cdotter]

I didn't see your post before hitting reply. Thank you, I'll check that out as well.