Linear Fractional Free Stable Motions and Selfsimilar Free Stable Processes

In classical probability theory, selfsimilar stable processes were well studied in the 1980s. Among others, the so-called linear fractional stable motion is a typical example of selfsimilar stable processes, including the well-known fractional Brownian motion as a special case. In this paper, the linear fractional stable motion and selfsimilar stable processes with stationary increments are studied within the framework of free probability.