Simply and multiply scaled diffusion limits for continuous time random walks

摘要: First a survey is presented on how space-time fractional diffusion processes can be obtained by well-scaled limiting from continuous time random walks under the sole assumption of asymptotic power laws (with appropriate exponents for tail behaviour waiting times and jumps). The spatial operator in pseudo-differential equation inverse general Riesz-Feller potential operator. analysis carried out via transforms Fourier Laplace. Then mixtures distributions, likewise jump are considered, it shown that correct multiple scaling limit yields equations with distributed order derivatives (fractional operators being replaced integrals over such ones, differentiation as variable integration). It outlined this way super-fast super-slow modelled.