The Markov property is the defining assumption of a Markov chain: the future depends on the current state, but not on the full past. It does not mean history is irrelevant; rather, it means that all relevant historical information is summarized by the present state.
Conditions: The process satisfies the Markov property.; The current state contains all information needed to determine future transition behavior.
The Markov property is the defining assumption of a Markov chain: the future depends on the current state, but not on the full past. It does not mean history is irrelevant; rather, it means that all relevant historical information is summarized by the present state.
Conditions: The process satisfies the Markov property.; The current state contains all information needed to determine future transition behavior.
A single probability distribution, such as a bell curve, describes uncertainty at one instant but cannot capture temporal dynamics. Markets evolve continuously: returns arrive sequentially, volatility changes, and extreme events cluster.
Conditions: The system being modeled changes over time.; Returns, volatility, or event clustering exhibit temporal structure.
A single probability distribution, such as a bell curve, describes uncertainty at one instant but cannot capture temporal dynamics. Markets evolve continuously: returns arrive sequentially, volatility changes, and extreme events cluster.
Conditions: The system being modeled changes over time.; Returns, volatility, or event clustering exhibit temporal structure.