Resumen de Stochastic geometric wave equations with values in compact Riemannian homogeneous spaces

Zdzislaw Brzezniak, Martin Ondreját

• Let M be a compact Riemannian homogeneous space (e.g., a Euclidean sphere). We prove existence of a global weak solution of the stochastic wave equation Dt∂tu=∑dk=1Dxk∂xku+fu(Du)+gu(Du)W˙ in any dimension d≥1, where f and g are continuous multilinear maps, and W is a spatially homogeneous Wiener process on Rd with finite spectral measure. A nonstandard method of constructing weak solutions of SPDEs, that does not rely on martingale representation theorem, is employed.