Geodesic
An extension of the It\^o integral: Toward a general theory of stochastic integration
Teoriâ slučajnyh processov, Tome 16 (2010) no. 1, pp. 17-28

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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, adapted stochastic process, Itô integral, Hitsuda-Skorokhod integral, anticipating, instantly independent stochastic processes, evaluation points, stochastic integral, stochastic differential equations.
Mots-clés : filtration, Itô's formula 
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     title = {An extension of the {It\^o} integral: {Toward} a general theory of stochastic integration},
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Wided Ayed; Hui-Hsiung Kuo. An extension of the It\^o integral: Toward a general theory of stochastic integration. Teoriâ slučajnyh processov, Tome 16 (2010) no. 1, pp. 17-28. http://geodesic.mathdoc.fr/item/THSP_2010_16_1_a2/