Stochastic foundation of normal and anomalous Cattaneo-type transport

We investigate the connection of the Cattaneo equation and the stochastic c ontinuous time random walk (CTRW) theory. We show that the velocity model i n a CTRW scheme is suited to derive the standard Cattaneo equation, and all ows, in principle. for a generalisation to anomalous transport. As a result for a broad waiting time distribution with diverging mean, we find a stron g memory to the initial condition of the system: The ballistic behaviour su bsists also for long times. Only if a characteristic waiting time exists, a non-ballistic, enhanced motion is found in the limit of long times. No tra nsition to subdiffusion can be found. (C) 1999 Elsevier Science B.V. All ri ghts reserved.