Ballistic diffusion induced by non-Gaussian noise

In this letter, we have analyzed the diffusive behavior of a Brownian particle subject to both internal Gaussian thermal and external non-Gaussian noise sources. We discuss two time correlation functions C (t) of the non-Gaussian stochastic process, and find that they depend on the parameter q, indicating the departure of the non-Gaussian noise from Gaussian behavior: for q <= 1, C (t) is fitted very well by the first-order exponentially decaying curve and approaches zero in the longtime limit, whereas for q > 1, C (t) can be approximated by a second-order exponentially decaying function and converges to a non-zero constant. Due to the properties of C (t), the particle exhibits a normal diffusion for q <= 1, while for q > 1 the non-Gaussian noise induces a ballistic diffusion, i.e., the long-time mean square displacement of the free particle reads <[x(t) - < x(t)>](2)> proportional to t(2).