The Itô-Henstock Stochastic Differential Equations

Abstract

In this paper, we study the stochastic integral equation with its stochastic integral defined using the Henstock approach, or commonly known as the generalized Riemann approach, instead of the classical Ito integral, which we shall call it the Ito-Henstock integral equation. Our aim is to prove the existence of solution of the Ito-Henstock integral equation using the well known method used in the existence theorem of the ordinary differential equation, namely the Picard’s iteration method.