CTRW Approximations for Fractional Equations with Variable Order

The standard diffusion processes are known to be obtained as the limits of appropriate random walks. These prelimiting walks can quite different, however. coefficient made responsible for size jumps or intensity jumps. limit does not feel difference. situation changes if we model jump-type approximations via CTRW with non-exponential waiting times. If make and take times from domain attraction an $$\alpha $$ -stable law a constant , then scaling would lead in small large intensities most fractional equation. However, choose fixed jump sizes use distinguish at different points, obtain equations variable position-dependent derivatives. In this chapter, build rigorously these prove their convergence corresponding cases multidimensional diffusions more general Feller processes.