Effects of Randomness on Power Law Tails in Multiplicatively Interacting Stochastic Processes

摘要

Effects of randomness on non-integer power law tails in multiplicativelyinteracting stochastic processes are investigated theoretically. Generally,randomness causes decrease of the exponent of tails and the growth rate ofprocesses. Explicit calculations are performed for two examples: uniformlydistributed and two peaked systems. Significant influence is demonstrated whena bare growth rate is low and coupling is weak. It should be emphasized thateven the sign of the growth rate can be changed from positive to negativegrowth.