An infinite continuous model which derives from a finite discrete model describing the time evolution of the density of firms

摘要

We derive a continuous model from a discrete model describing the time evolution of the density of firms which attempt to relocate within a bounded domain in order to obtain higher desirability in business. The discrete model consists of a finite number of firms, and is discretized with respect to both the time variable and the space variable. In the mathematical level of rigor, we derive the continuous model from the finite discrete model, by making use of a certain method frequently employed in statistical physics. We can consider that the continuous model thus obtained consists of an infinite number of firms. The infinite continuous model is represented by a non-linear integro-partial differential equation called the master equation.