Multilevel Monte Carlo estimators for elliptic PDEs with Lévy-type diffusion coefficient

General elliptic equations with spatially discontinuous diffusion coefficients may be used as a simplified model for subsurface flow in heterogeneous or fractured porous media. In such model, data sparsity and measurement errors are often taken into account by randomization of the coefficient equation which reveals necessity construction flexible, random fields. Subordinated Gaussian fields functions on higher dimensional parameter domains sample paths great distributional flexibility. present work, we consider partial differential (PDE) where subordinated occur coefficient. Problem specific multilevel Monte Carlo (MLMC) Finite Element methods constructed to approximate mean solution PDE. We prove a-priori convergence standard MLMC estimator modified - Control Variate validate our results various numerical examples.