Spatial quadratic variations for the solution to a stochastic partial differential equation with elliptic divergence form operator

Modern Stochastics: Theory and Applications

Mounir Zili¹  Eya Zougar¹ 

[1] University of Monastir, Faculty of sciences of Monastir, Department of Mathematics, LR18ES17, Avenue de l’environnement, 5019 Monastir, Tunisia;

关键词: stochastic partial differential equations;    divergence form;    piecewise constant coefficients;    fundamental solution;    Stein-Malliavin calculus;    almost sure central limit theorem;   

DOI  :  10.15559/19-VMSTA139

来源: DOAJ

【 摘 要 】

We introduce a stochastic partial differential equation (SPDE) with elliptic operator in divergence form, with measurable and bounded coefficients and driven by space-time white noise. Such SPDEs could be used in mathematical modelling of diffusion phenomena in medium consisting of different kinds of materials and undergoing stochastic perturbations. We characterize the solution and, using the Stein–Malliavin calculus, we prove that the sequence of its recentered and renormalized spatial quadratic variations satisfies an almost sure central limit theorem. Particular focus is given to the interesting case where the coefficients of the operator are piecewise constant.

【 授权许可】

Unknown