The existence and uniqueness of solutions for a system of stochastic differential equations with non-lipschitz coefficients

Abstract

This paper aims to study the existence and uniqueness of solutions for a system of stochastic differential equations (SSDEs) with non-Lipschitz coefficients. By employing the Picard iterative method, we show the existence of solutions for SSDEs with non-Lipschitz coefficients under mild assumptions. According to the stopping time, we obtain the explosiveness of solutions for SSDEs with non-Lipschitz coefficients. Moreover, by using the Bihari inequality, we prove the uniqueness of the solution for SSDEs with non-Lipschitz coefficients.