The Itô-Henstock stochastic differential equations. (English) Zbl 1322.60126

Summary: 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 Itō integral, which we shall call the Itō-Henstock integral equation. Our aim is to prove the existence of solution of the Itō-Henstock integral equation using the well known method used in the existence theorem for ordinary differential equations, namely the Picard iteration method.


60H20 Stochastic integral equations
60H10 Stochastic ordinary differential equations (aspects of stochastic analysis)
60H05 Stochastic integrals
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