Henstock's Version of Itô's Formula

Abstract

Itô's Formula is the stochastic analogue of the change of variable formula for deterministic integrals. It is a useful tool in dealing with stochastic integration. In this paper, using Henstock's approach, we derive two versions of Itô's Formula. Henstock's or generalized Riemann approach has been successful in giving an alternative definition of stochastic integral, which is more explicit, intuitive and less measure theoretic. Henstock's approach provides a simpler and more direct proof of Itô's Formula, although we do not claim that it is a generalization of the classical results.