Let (Ω,F,P) be a probability space and Y a random variable such that E Y 2 ⊂ F be a σ-algebra. Show that Consider a discrete state-space HMM. Denote by X = {1,...,m} the statespace of the Markov...

Let (Ω,F,P) be a probability space and Y a random variable such that E Y
²
<>⊂ F be a σ-algebra. Show that

Consider a discrete state-space HMM. Denote by X = {1,...,m} the statespace of the Markov chain, M, the m × m transition matrix and, for y ∈ Y, by Γ = diag(G(1, y),...,G(m,Y)). Assume that M admits a unique stationary distribution denoted by π = [π(1),...,π(m)].