Agent based reasoning for the non-linear stochastic models of long-range memory

We extend Kirman's model by introducing variable event time scale. The proposed flexible time scale is equivalent to the variable trading activity observed in financial markets. Stochastic version of the extended Kirman's agent based model is compared to the non-linear stochastic models of long-range memory in financial markets. Agent based model providing matching macroscopic description serves as a microscopic reasoning of the earlier proposed stochastic model exhibiting power law statistics.