Skip to content

IAI Actuarial Core Principles · Risk Modelling and Survival Analysis · Markov processes

A discrete-time Markov chain on states {1,2,3,4} has transition matrix rows: state 1: (0.5, 0.5, 0, 0); state 2: (0.4, 0.6, 0, 0); state 3: (0, 0, 0.3, 0.7); state 4: (0.2, 0.2, 0.3, 0.3). Which statement about the classes of this chain is correct?

{1,2} is closed because no transitions leave it, while states 3 and 4 communicate with each other but can leak into {1,2}, so their class is not closed and those states are transient.

  1. AThe chain is irreducible because every state has some outgoing transition
  2. B{1,2} is a closed class and {3,4} is also a closed class
  3. C{1,2} is a closed class, and states 3 and 4 are in a single non-closed communicating classCorrect
  4. DStates 3 and 4 are absorbing states
  5. {1,2} is not closed because state 4 leads into it

Explanation

From states 1 and 2 the chain can only reach 1 and 2, so {1,2} is closed. State 3 reaches 4 and state 4 reaches 3, so they communicate. State 4 can also move to 1 or 2 and never returns, so {3,4} is not closed. Option 4 confuses entry into a class with leaving it.

Did you get it right without looking?

One question tells you little. A timed set on Markov processes shows your real accuracy, how long you take and where you lose marks.

Practise Markov processesFree diagnostic mock

More Markov processes questions