Les modèles non linéaires à effets mixtes - Isped

Convergence of the algorithm
(Kuhn and Lavielle)
C1 The chain (φ k ) k≥0 takes its values in a compact subset E of R l .
C2 For any compact subset V of Θ, there exists a real constant L such
that for any (θ, θ ′ ) in V 2
sup |Π θ (x, y) − Π θ ′(x, y)| ≤ L|θ − θ ′ |.
(x,y)∈E 2
C3 The transition probability Π θ generates a uniformly ergodic chain
whose invariant probability is p(·|y; θ): there exists K θ ∈ R + and
ρ θ ∈]0, 1[ such that
∀φ ∈ E, ∀k ∈ N, ||Π k θ (φ, ·) − p(·|y; θ)|| T V ≤ K θ ρ k θ ,
K sup
θ
K θ < +∞ and ρ sup
θ
ρ θ < 1.
Sminaire ”Statistique et Sant Publique”, Bordeaux - 8 novembre 2005, p.30