Stochastic Model of Trend Dynamics and a Density Dependent Population Process with Discontinuity,

#### V.V. Scherbakov

2003, v.9, Issue 3, 469-486

ABSTRACT

The paper is motivated by studying a multidimensional Markov process describing the behaviour of a group of trading or voting people. Each coordinate (component) of the process has two states, $\{0\}$ and $\{1\}$. The transition rates of the process depend on the total sum of components in a discontinuous way. We are interested in asymptotic analysis of the behaviour of the process as the number of components goes to infinity. The analysis is reduced to proving the law of large numbers for a density dependent population process with discontinuity.

Keywords: density dependent populationprocess,voter model,mean field,random walk,law of large numbers