Perturbation of Ornstein-Uhlenbeck stationary distributions: expansion and simulation

Emmanuel Gobet (1) , Qihao She (2)

1 CMAP - Centre de Mathématiques Appliquées - Ecole Polytechnique
2 Nanyang Technological University [Singapour]

We consider a multidimensional stochastic differential equation Y written as a drift-perturbation of an ergodic Ornstein-Uhlenbeck process X. Under the condition of time-reversibility of X, we derive a first and second order expansion of the stationary distribution µ^Y of Y in terms of X. Error estimates are established. These approximations are then turned into a simulation scheme for sampling approximately according to µ Y. Numerical experiments support the theoretical error estimates.

Mots clés: ergodic diffusion; invariant measure; time-reversibility; perturbation method; asymptotic expansion

Domaines: Probabilités [math.PR]

Emmanuel Gobet, Qihao She. Perturbation of Ornstein-Uhlenbeck stationary distributions: expansion and simulation. 2016. ⟨hal-01345926⟩