The nonlinear stochastic behavior of chaotic inflation is characterized by the 'scaling' effect. Using a simple criterion for the appearance of scaling behavior in the λϕ4 λϕ4 inflation model, we show explicitly that in this limit the onset of the scaling regime does not require any special initial conditions and that it is independent of the self-coupling constant λ λ . Non-Gaussian statistics in adiabatic fluctuations are important only for super-horizon scales and the scaling regime does not lead to any significant statistical properties on currently observable scales. However, the scaling effect gives some cosmological consequences very different from what we expect in the naive diffusion approximation for quantum fluctuations. The classical (deterministic) treatment of the inflation field (essentially a quantum mechanical object.) becomes valid towards the end of inflation.