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Theory of Stochastic Processes, 2010, Volume 16(32), Issue 1, Pages 17–28 (Mi thsp56)  
An extension of the Itô integral: Toward a general theory of stochastic integration

Wided Ayeda, Hui-Hsiung Kuob

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
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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.
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Document Type: Article
MSC: Primary 60H05, 60H20; Secondary 60H40
Language: English
Citation: Wided Ayed, Hui-Hsiung Kuo, “An extension of the Itô integral: Toward a general theory of stochastic integration”, Theory Stoch. Process., 16(32):1 (2010), 17–28
Citation in format AMSBIB
\Bibitem{AyeKuo10}
\by Wided Ayed, Hui-Hsiung Kuo
\paper An extension of the It\^o integral: Toward a general theory of stochastic integration
\jour Theory Stoch. Process.
\yr 2010
\vol 16(32)
\issue 1
\pages 17--28
\mathnet{http://mi.mathnet.ru/thsp56}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=2779844}
\zmath{https://zbmath.org/?q=an:1224.60122}
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