A generic construction for high order approximation schemes of semigroups using random grids

Our aim is to construct high order approximation schemes for general semigroups of linear operators P_t,t≥ 0 . In order to do it, we fix a time horizon T and the discretization steps h_l=T/n^l,l∈ℕ and we suppose that we have at hand some short time approximation operators Q_l such that P_h_l=Q_l+O(h_l^1+α) for some α >0 . Then, we consider random time grids Π (ω )={t_0(ω )=0更多