Economics of a Master Equation and Eluctuations
The real-world economy actually seems to be irrelevant to the EMH. The interaction of heterogeneous factors inside and outside markets may generate many complicated outcomes for the world economy.
This resembles the movements of exchangeable agents in a combinatorial stochastic process like the urn process. The stochastic evolution of the state vector can be described in terms of the master equation equivalent to the Chapman-Kolmogorov differential equation system. The master equation leads to aggregate dynamics, from which the Fokker-Planck equation can be derived, so we can explicitly argue the fluctuations in a dynamic system. These settings are made feasible by classifying agents in the system by type and tracking the variations in cluster size. In Figs. 1.9 and 1.10,1 show the images of a master equation as well as stochastic trajectories, probability distribution and quasi-mean values in a phase transition from mono- to fez-stability.
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