Wided Ayed, Hui-Hsiung Kuo, “An extension of the Itô integral: Toward a general theory of stochastic integration”, Theory Stoch. Process., 2010, Volume 16(32), Issue 1,Pages <nobr>17

An extension of the Itô integral: Toward a general theory of stochastic integration

Wided Ayed^a, Hui-Hsiung Kuo^b

^a Department of Mathematics, Institut Préparatoire aux Etudes d'Ingénieurs, El Merezka, Nabeul, 8058, Tunisia
^b Department of Mathematics, Louisiana State University, Baton Rouge, LA 70803, USA

Abstract: We introduce the class of instantly independent stochastic processes, which serves as the counterpart of the Itô theory of stochastic integration. This class provides a new approach to anticipating stochastic integration. The evaluation points for an adapted stochastic process and an instantly independent stochastic process are taken to be the left endpoint and the right endpoint, respectively. We present some new results on Itô's formula and stochastic differential equations.

Keywords: Brownian motion, filtration, adapted stochastic process, Itô integral, Hitsuda-Skorokhod integral, anticipating, instantly independent stochastic processes, evaluation points, stochastic integral, Itô's formula, stochastic differential equations.

MSC: Primary 60H05, 60H20; Secondary 60H40

Language: English