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Martingale structure of Skorohod integral processes. (English) Zbl 1134.60039

The article is devoted to the investigation of the structure of the process \[ Y_t=\int _0^tu_s\,dX_s, \] where \(X\) is the standard Brownian motion and the integral is considered in the Skorokhod sense. The authors prove that \(Y\) can be approximated by the sums of products of forward and backward Ito integrals with respect to \(X.\) Also the article contains the optional sampling theorem for \(Y\) under the assumption that \(u\) has stochastic derivatives.

MSC:

60H05 Stochastic integrals
60H07 Stochastic calculus of variations and the Malliavin calculus
60G15 Gaussian processes
60H10 Stochastic ordinary differential equations (aspects of stochastic analysis)
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