Consider the chain in Example 1.2-5 and set f k = P( i = k), k =

Consider the chain in Example 1.2-5 and set f_k = P(ξ_i = k), k = 0,1, ... . (This probability is the same for all i). Find the transition matrix.

Example 1.2-5

Let X_t = max{ξ₀, ξ₁, ..., ξ_t}. Clearly,

and (1.2.5) holds for g(m,n) = max{m,n}. In Exercise 5, it is suggested to the reader to find the transition matrix for such a chain.