  Effects of randomness on non-integer power law tails in multiplicatively
interacting stochastic processes are investigated theoretically. Generally,
randomness causes decrease of the exponent of tails and the growth rate of
processes. Explicit calculations are performed for two examples: uniformly
distributed and two peaked systems. Significant influence is demonstrated when
a bare growth rate is low and coupling is weak. It should be emphasized that
even the sign of the growth rate can be changed from positive to negative
growth.
