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Markov chains are used not because markets are memoryless, but because they capture persistence, regime behaviour, and long-run risk with minimal assumptions. They sit between pure randomness and full determinism, offering a balance of being simple enough to analyse yet rich enough to matter.

Conditions: Used as a modelling framework rather than as an exact description of markets.; The goal is parsimonious representation of persistence and regime changes.

Markov chains are used not because markets are memoryless, but because they capture persistence, regime behaviour, and long-run risk with minimal assumptions. They sit between pure randomness and full determinism, offering a balance of being simple enough to analyse yet rich enough to matter.

Conditions: Used as a modelling framework rather than as an exact description of markets.; The goal is parsimonious representation of persistence and regime changes.

An absorbing state is a state that, once entered, cannot be left. It is characterized by a transition probability of 1 to itself.

Conditions: Transition probability from the state to itself must be exactly 1.; The system eventually enters an absorbing state if reachable.

An absorbing state is a state that, once entered, cannot be left. It is characterized by a transition probability of 1 to itself.

Conditions: Transition probability from the state to itself must be exactly 1.; The system eventually enters an absorbing state if reachable.