Quadratic stochastic operator on infinite state space and the application in economy

Abstract

The motivation of the theory of quadratic stochastic operator (QSO) arises from some problem of heredity as first introduced by Bernstein in 1924. It is known there are many systems which can be described by this operator. At present, the theory of quadratic stochastic operator (QSO) defined on finite state space is well executed. Hence, the focus in this thesis is mainly the construction of quadratic stochastic operator (QSO) on infinite state space. A general problem in this theory is to study the limit behaviour of the trajectory in term of initial state (point). Some applications of the QSO in economic field are constructed where the correlation between Nash equilibrium and path limit behavior with the dynamic of quadratic stochastic operators are provided.