Ergodic approximation of the distribution of a stationary diffusion : rate of convergence

Gilles Pagès (1) , Fabien Panloup (2)

1 LPMA - Laboratoire de Probabilités et Modèles Aléatoires
2 IMT - Institut de Mathématiques de Toulouse UMR5219

We extend to Lipschitz continuous functionals either of the true paths or of the Euler scheme with decreasing step of a wide class of Brownian ergodic diffusions, the Central Limit Theorems formally established for their marginal empirical measure of these processes (which is classical for the diffusions and more recent as concerns their discretization schemes). We illustrate our results by simulations in connection with barrier option pricing.

Mots clés: stochastic differential equation; stationary process; steady regime; ergodic diffusion; Central Limit Theorem; Euler scheme

Domaines: Probabilités [math.PR]

Gilles Pagès, Fabien Panloup. Ergodic approximation of the distribution of a stationary diffusion : rate of convergence. The Annals of Applied Probability, 2012, 22 (3), pp.1059-1100. ⟨10.1214/11-AAP779⟩. ⟨hal-00512722⟩