  From a simple path integral involving a variable volatility in the velocity
differences, we obtain velocity probability density functions with exponential
tails, resembling those observed in fully developed turbulence. The model
yields realistic scaling exponents and structure functions satisfying extended
self-similarity. But there is an additional small scale dependence for
quantities in the inertial range, which is linked to a slow approach to
Kolmogorov (1941) scaling occurring in the large distance limit.
