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

Boon, Tan Soon; Lam, Toh Tin

Real Anal. Exch. 37(2011-2012), No. 2, 411-424 (2012).

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.

MSC:

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

Keywords:

Itō-Henstock stochastic integral equation; stochastic differential equation; existence theorem; Picard iteration method

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