%0 Journal Article %T A generic construction for high order approximation schemes of semigroups using random grids %+ Mathematical Risk Handling (MATHRISK) %+ Centre d'Enseignement et de Recherche en Mathématiques et Calcul Scientifique (CERMICS) %+ Laboratoire d'Analyse et de Mathématiques Appliquées (LAMA) %A Alfonsi, Aurélien %A Bally, Vlad %Z Aurélien Alfonsi benefited from the support of the “Chaire Risques Financiers”, Fondation du Risque. %< avec comité de lecture %@ 0029-599X %J Numerische Mathematik %I Springer Verlag %8 2021 %D 2021 %Z 1905.08548 %R 10.1007/s00211-021-01219-2 %K Random grids %K Parametrix %K Monte-Carlo methods %K Approximation schemes %Z AMS: 60H35, 65C30, 65C05, 65C20 %Z Mathematics [math]/Probability [math.PR]Journal articles %X Our aim is to construct high order approximation schemes for general semigroups of linear operators $P_{t},t\geq 0$. In order to do it, we fix a time horizon $T $ and the discretization steps $h_{l}=\frac{T}{n^{l}},l\in \mathbb{N}$ and we suppose that we have at hand some short time approximation operators $Q_{l}$ such that $P_{h_{l}}=Q_{l}+O(h_{l}^{1+\alpha })$ for some $\alpha >0$. Then, we consider random time grids $\Pi (\omega )=\{t_0(\omega )=0