  We construct a general stochastic process and prove weak convergence results.
It is scaled in space and through the parameters of its distribution. We show
that our simplified scaling is equivalent to time scaling used frequently. The
process is constructed as an integral with respect to a Poisson random measure
which governs several parameters of trading agents in the context of stock
prices. When the trading occurs more frequently and in smaller quantities, the
limit is a fractional Brownian motion. In contrast, a stable Levy motion is
obtained if the rate of trading decreases while its effect rate increases.
