Skorokhod Integral
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High Quality Content by WIKIPEDIA articles! Consider a fixed probability space ( , , P) and a Hilbert space H; E denotes expectation with respect to P: mathbf{E} [X] : int_{Omega} X(omega) , mathrm{d} mathbf{P}(omega). Intuitively speaking, the Malliavin derivative of a random variable F in Lp( ) is defined by expanding it in terms of Gaussian random variables that are parametrized by the elements of H and differentiating the expansion formally; the Skorokhod integral is the adjoint operation to the Malliavin derivative. Consider a family of R-valued random variables W(h), indexed by the…mehr

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High Quality Content by WIKIPEDIA articles! Consider a fixed probability space ( , , P) and a Hilbert space H; E denotes expectation with respect to P: mathbf{E} [X] : int_{Omega} X(omega) , mathrm{d} mathbf{P}(omega). Intuitively speaking, the Malliavin derivative of a random variable F in Lp( ) is defined by expanding it in terms of Gaussian random variables that are parametrized by the elements of H and differentiating the expansion formally; the Skorokhod integral is the adjoint operation to the Malliavin derivative. Consider a family of R-valued random variables W(h), indexed by the elements h of the Hilbert space H. Assume further that each W(h) is a Gaussian (normal) random variable, that the map taking h to W(h) is a linear map, and that the mean and covariance structure is given by mathbf{E} [W(h)] = 0, mathbf{E} [W(g)W(h)] = langle g, h rangle_{H},