Markov models capture systems that transition probabilistically between a finite set of states.
One application in finance are Bond credit ratings. A "AAA" bond has a 95% every year of retaining it's high credit rating but there is a 5% of it being downgraded to "AA". In similar vein a "CCC" bond has a probability to be upgraded to "B" or go into default. Credit analysts construct a table of transition probabilities to gain a helicopter view of the bond markets.
A Markov process can converge into a unique statistical equilibrium if it satisfies four conditions :
a) It has a finite set of states.
b) Probabilities of transition between each state is fixed.
c) The system can get from any state or any other state through a series of transitions.
d) The system does not produce a deterministic cycle through a sequence of states.
If only these four conditions are met, the number of bonds
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