IAI Actuarial Core Principles · Risk Modelling and Survival Analysis · Markov chains
Which statement best describes the Markov property for a discrete-time stochastic process (X_n)?
The Markov property means that once the current state is known, the distribution of the next state does not depend on how the process reached that state. The past adds no further information about the future beyond the present state.
- AGiven the present state, the conditional distribution of the next state does not depend on the earlier history of the processCorrect
- BThe process returns to every state infinitely often with probability one
- CThe transition probabilities must be the same at every time step
- DThe future states are independent of the present state
- The process has a unique stationary distribution
Explanation
The Markov property says that, conditional on the present state, the past and future are independent. Time-homogeneity (option 2) is a separate property, and independence from the present state (option 3) would describe an independent sequence, not a Markov chain.
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