The assumption that transport in a Hamiltonian system can be described as a normal diffusion process leads naturally to a power law dependence of the exit time, $T_E$, to the Lyapunov time, $T_L = 1/\lambda$, where by $\lambda$ we denote the maximal Lyapunov Characteristic Number, LCN. Since transport in perturbed integrable Hamiltonian systems can be modelled as normal diffusion only in regions where most of the KAM tori are destroyed, the power law dependence appears when the perturbation is strong. In this way the dependence $T_E \sim T_L^c, c \approx 1.75$, found numerically by Murison et al. (1994) for the motion of asteroids in the outer belt, can be naturally interpreted, since in this region it is well known that resonances are closely spaced and, therefore, it is expected that KAM tori are mostly destroyed. However there is no theoretical reason why the exponent c, should have a universal value.
Key words: Invariant tori, overlapping of resonances, Lyapunov exponents, random walk, Levy flights, diffusion coefficient.