  Effects of non-Gaussian $\alpha-$stable L\'evy noise on the Gompertz tumor
growth model are quantified by considering the mean exit time and escape
probability of the cancer cell density from inside a safe or benign domain. The
mean exit time and escape probability problems are formulated in a
differential-integral equation with a fractional Laplacian operator. Numerical
simulations are conducted to evaluate how the mean exit time and escape
probability vary or bifurcates when $\alpha$ changes. Some bifurcation
phenomena are observed and their impacts are discussed.
