(Functional autoregressive process). Consider the following recursion a) Determine the Markov kernel of this chain. (b) Assume that the distribution of Z 0 has a density q with respect to Lebesgue’s...

(Functional autoregressive process). Consider the following recursion

a) Determine the Markov kernel of this chain.

(b) Assume that the distribution of Z₀
has a density q with respect to Lebesgue’s measure on R; show that the Markov kernel P has a density. Give the expression of this density

(Setwise convergence / existence of a stationary distribution). Assume that