John Mount has some thoughts for us:
I want to collect some “great things to know about linear Markov chains.”
For this note we are working with a Markov chain on states that are the integers
0
throughk
(k > 0
). A Markov chain is an iterative random process with time tracked as an increasing integert
, and the next state of the chain depending only on the current (soon to be previous) state. For our linear Markov chain the only possible next states from statei
are:i
(called a “self loop” when present),i+1
(called up or right), andi-1
(called down or left). In no case does the chain progress below0
or abovek
.
Click through for notes on two variants of this sort of linear Markov chain, as well as a pair of appendices containing derivation notes and Python code.
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