Carathéodory's approximate solution to stochastic differential delay equation


Yeol Je Cho - Department of Mathematics Education and the RINS, Gyeongsang National University, Jinju 660-701, Republic of Korea.
Young-Ho Kim - Department of Mathematics, Changwon National University, Changwon 641-773, Republic of Korea.


In this paper, we show the difference between an approximate solution and an accurate solution for a stochastic differential delay equation, where the approximate solution, which is called by Carathéodory, is constructed by successive approximation. Furthermore, we study the p-th moment continuity of the approximate solution for this delay equation.