Stochastic differential equations with biased space-averaging operators

Abstract

A fundamental problem in the population growth is how to capture the space-averaging dependence. In this paper, we consider a class of stochastic differential equations with biased space-averaging operators which can be used to describe the space-averaging dependence. The existence and uniqueness for strong solutions are investigated and the comparison theorem is derived under some mild conditions. Furthermore, the non-confluent property for strong solutions is also given.