Weak approximation of averaged diffusion processes

Emmanuel Gobet (1) , Mohammed Miri (2)

1 CMAP - Centre de Mathématiques Appliquées - Ecole Polytechnique
2 Pricing Partners

We derive expansion results in order to approximate the law of the average of the marginal of diffusion processes. The average is computed w.r.t. a general parameter that is involved in the diffusion dynamics. Our approximation is based on the use of proxys with normal distribution or log-normal distribution, so that the expansion terms are explicit. We provide non asymptotic error bounds, which justifies the expansion accuracy as the time or the diffusion coefficients are small in a suitable sense.

Domaines: Probabilités [math.PR]

Emmanuel Gobet, Mohammed Miri. Weak approximation of averaged diffusion processes. Stochastic Processes and their Applications, 2014, 124, pp.475--504. ⟨hal-00618470⟩