In determining steady-state behavior for a process with absorbing states, the subdivision of the transition matrix yields:
A)an identity submatrix, but no zero submatrix.
B)no identity submatrix, but a zero submatrix.
C)both an identity submatrix and a zero submatrix.
D)neither an identity submatrix nor a zero submatrix.

Question

Quizplus · Accepted Answer

In the context of Markov chains, when analyzing processes with absorbing states, the transition matrix is often rearranged into a canonical form. This form subdivides the matrix into four blocks: an identity matrix (representing the absorbing states), a zero matrix (indicating that absorbing states do not transition back to transient states), and two other matrices representing transitions between transient states and from transient states to absorbing states. This structure is crucial for analyzing steady-state behavior and calculating absorption probabilities.

In Determining Steady-State Behavior for a Process with Absorbing States