Convergence rate of strong approximations of compound random maps

Emmanuel Gobet (1) , Mohamed Mrad (2)

1 CMAP - Centre de Mathématiques Appliquées - Ecole Polytechnique
2 LAGA - Laboratoire Analyse, Géométrie et Applications

We consider a random map x → F (ω, x) and a random variable Θ(ω), and we denote by F^N (ω, x) and Θ^N (ω) their approximations: We establish a strong convergence result, in Lp-norms, of the compound approximation F^N (ω, Θ^N (ω)) to the compound variable F (ω, Θ(ω)), in terms of the approximations of F and Θ. We then apply this result to the composition of two Stochastic Differential Equations through their initial conditions, which can give a way to solve some Stochastic Partial Differential Equations.

Mots clés: strong approximation; Garsia-Rodemich-Rumsey lemma; Euler schemes; stochastic flow

Domaines: Probabilités [math.PR]

Emmanuel Gobet, Mohamed Mrad. Convergence rate of strong approximations of compound random maps. Discrete & Continuous Dynamical Systems- Series-B, 2018. ⟨hal-01141320v2⟩