Approximate Solutions of Set-Valued Stochastic Differential Equations

Abstract In this paper, we consider the problem of approximate solutions of set-valued stochastic differential equations. We firstly prove an inequality of set-valued Itô integrals, which is related to classical Itô isometry, and an inequality of set-valued Lebesgue integrals. Both of the inequalities play an important role to discuss set-valued stochastic differential equations. Then we mainly state the Carathodory's approximate method and the Euler-Maruyama's approximate method for set-valued stochastic differential equations. We also investigate the errors between approximate solutions and accurate solutions