Weak Averaging of Semilinear Stochastic Differential Equations with Almost Periodic Coefficients

Mikhail Kamenski (1) , Omar Mellah (2) , Paul Raynaud de Fitte (2)

1 Departement of Mathematics (VSU) State University of Voronezh
2 LMRS - Laboratoire de Mathématiques Raphaël Salem

An averaging result is proved for stochastic evolution equations with highly oscillating coefficients. This result applies in particular to equations with almost periodic coefficients. The convergence to the solution of the averaged equation is obtained in distribution, as in previous works by Khasminskii and Vrkoč.

Mots clés: averaging methods; stochastic evolution equations; almost periodic solutions; Wasserstein distance

Domaines: Probabilités [math.PR]; Analyse fonctionnelle [math.FA]

Mikhail Kamenski, Omar Mellah, Paul Raynaud de Fitte. Weak Averaging of Semilinear Stochastic Differential Equations with Almost Periodic Coefficients. 2013. ⟨hal-00746193v4⟩