Question

For a Markov process
uₜ=rhouₜ₋₁+vₜ with |rho|<1
and random variables vₜ are such that E(vt)=0,Var(vₜ)=σ2/8 and Cov(vₜ,vs)=0 for t≠s.
Show that :
(i) ut=∑[infinity]ᵣ₌₀ rhoʳvₜ₋ᵣ