The q -Gaussian distribution is also obtained as the asymptotic probability density function of the position of the unidimensional motion of a mass subject to two forces: a deterministic force of the type F 1 ( x ) = − − 2 x / ( 1 − − x 2 ) (determining an infinite potential well) and a stochastic white noise force F 2 ( t ) = 2 ( 1 − − q ) ξ ξ ( t ) , where ξ ξ ( t ) is a white noise. Note that in the overdamped/small mass approximation the above-mentioned convergence fails for q < 0 , as recently shown.