Una generalizzazione del processo di Ehrenfest

The core of the method of Statistical Mechanics is that of studyingthe macroscopic properties at our human scale in terms of the properties of the microscopic constituents (Jancel 1969). A similar aim affects some new approaches to macroeconomic modeling (Aoki 1996), that have been developed in order to describe macroscopic variables in terms of the behavior of a large collection of microeconomic entities (agents, price elements,...). These entities are supposed to change their state unceasingly, ruled by a probabilistic dynamics represented by jump Markov chains. Relationships among economic variables are statistical in an essential way, and are not made so by having additive disturbance or measurement errors superimposed on deterministic relationships.(Aoki 1996). In this work we want give an exact model able to unify a large extent of hypotheses introduced in this approach (Kelly 1979, Kirman 1993, Aoki 1999). Our treatise starts from the most known discrete model of Classical Statistical Physics (complementary to the continuous Brownian Motion), that is the celebrated stochastic process envisaged by Paul and Tatiana Ehrenfest at the beginning of this century. The main generalization we perform consists in introducing choice correlations between agents, that give raise to "herd behavior" if they are strong and positive.