  We develop walk-on-sphere for fractional Poisson equations with Dirichilet
boundary conditions in high dimensions. The walk-on-sphere method is based on
probabilistic represen tation of the fractional Poisson equation. We propose
effcient quadrature rules to evaluate integral representation in the ball and
apply rejection sampling method to drawing from the computed probabilities in
general domains. Moreover, we provide an estimate of the number of walks in the
mean value for the method when the domain is a ball. We show that the number of
walks is increasing in the fractional order and the distance of the starting
point to the origin. We also give the relationship between the Green function
of fractional Laplace equation and that of the classical Laplace equation.
Numerical results for problems in 2-10 dimensions verify our theory and the
effciency of the modified walk-on-sphere method.
