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We analyze two special socio-economic processes which are essentially determined by stochastic effects. In the first part we discuss a typical discrete stochastic process. We analyze the stochastic influences on new technologies in the process of competition on the market 1). We show, that stochastic effects may have important consequences for the fate of new technologies, if the advantage of the NEW is not very large. In the framework of linear rate theory, stochastic selection is very vague and has a broad region of neutrality. In order to win the competition the NEW needs big advantage. Technologies with nonlinear growth rates (hypercyclic systems) have only a chance to win in small niches, or with external support. This is the only way to overcome once-forever selection.
In the second part we study the closely related process of continuous transitions to a different technology. Here a completely different stochastic formalism based on Langevin- and Fokker-Planck equations is most appropriate 2). We explain the concept of active Brownian motion as a new tool of stochastic and nonlinear dynamics theory, and give several examples. We show that this model may also be used for describing the transitions between technologies in a continuous feature space 3) . The technologies are modeled as Brownian particles with velocity-dependent friction, collective interactions and external confinement. We simulate the dynamics of such transitions by a Langevin approach and estimate the transition rates.
References: 1) E. Bruckner, W. Ebeling, M.A. Jimenez-Montano, A. Scharnhorst, J. Evol. Econ. 6, 1-30 (1996); I. Hartmann, A. Scharnhorst, W. Ebeling, arXiv condmat /0406425 v. 1 18 June 2004. 2) F. Schweitzer, W, Ebeling, B. Tilch, Phys. Rev. Lett. 80, 5044 (1998). U. Erdmann et al., Eur. Phys. J. B 15, 105 (2000) 3) W. Ebeling, A. Neiman, L. Schimansky-Geier, A. Scharnhorts, Fluctuation and Noise Letters, to be published. |