As shown in Example 2, is not a regular stochastic matrix. Show that acts like a stable

Question:

As shown in Example 2,

is not a regular stochastic matrix. Show that

acts like a stable distribution for this matrix, and explain why this fact does not contradict the main premise of this section?

Distribution
The word "distribution" has several meanings in the financial world, most of them pertaining to the payment of assets from a fund, account, or individual security to an investor or beneficiary. Retirement account distributions are among the most...