Technological Innovation and Diffusion, Fluctuations and Growth (II): Deterministic and Stochastic Laws of Motion

In the following Part II the deterministic and stochastic laws of motion arising from the processes depicted in Part I (particulary Section 2), are analyzed in detail. In section 4 we study the typical non-linear logistic model emerging as the deterministic equivalent of the diffusion processes of Sections 2.3 and 2.4. The interaction of firm size and firm number are also studied within the same Section. In Section 5 we analyze the (asymptotic) stochastic laws of motion of the system. In particular, we study the Langevin equation and the approximations of the Fokker-Planck equations equivalent of the master equations of the same stochastic processes. We see that stochastic laws of motion may not be equivalent (not even asymptotically) to deterministic ones (e.g. Due to variance effects which determine increasingly larger fluctuations).