We propose and analyse randomized cubature formulae for the numerical integration of functions with respect to a given probability measure μ defined on domain Γ⊆Rd, in any dimension d. Each formula is exact finite-dimensional subspace Vn⊂L2(Γ,μ) n, uses pointwise evaluations integrand function ϕ:Γ→R at m>n independent random points. These points are drawn from suitable auxiliary that depends Vn...
