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- W2781692913 abstract "Asymptotic expansion of the distribution of a perturbation $Z_n$ of a Skorohod integral jointly with a reference variable $X_n$ is derived. We introduce a second-order interpolation formula in frequency domain to expand a characteristic functional and combine it with the scheme developed in the martingale expansion. The second-order interpolation and Fourier inversion give asymptotic expansion of the expectation $E[f(Z_n,X_n)]$ for differentiable functions $f$ and also measurable functions $f$. In the latter case, the interpolation method connects the two non-degeneracies of variables for finite $n$ and $infty$. Random symbols are used for expressing the asymptotic expansion formula. Quasi tangent, quasi torsion and modified quasi torsion are introduced in this paper. We identify these random symbols for a certain quadratic form of a fractional Brownian motion and for a quadratic from of a fractional Brownian motion with random weights. For a quadratic form of a Brownian motion with random weights, we observe that our formula reproduces the formula originally obtained by the martingale expansion." @default.
- W2781692913 created "2018-01-12" @default.
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- W2781692913 date "2017-12-30" @default.
- W2781692913 modified "2023-09-25" @default.
- W2781692913 title "Asymptotic expansion of Skorohod integrals" @default.
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- W2781692913 doi "https://doi.org/10.48550/arxiv.1801.00120" @default.
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