Weak convergence of the Stratonovich integral with respect to a class of Gaussian processes |
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Authors: | Daniel Harnett David Nualart |
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Institution: | Department of Mathematics, University of Kansas, 405 Snow Hall, Lawrence, KS 66045-2142, United States |
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Abstract: | For a Gaussian process X and smooth function f, we consider a Stratonovich integral of f(X), defined as the weak limit, if it exists, of a sequence of Riemann sums. We give covariance conditions on X such that the sequence converges in law. This gives a change-of-variable formula in law with a correction term which is an Itô integral of f? with respect to a Gaussian martingale independent of X. The proof uses Malliavin calculus and a central limit theorem from Nourdin and Nualart (2010) 8]. This formula was known for fBm with H=1/6 Nourdin et al. (2010) 9]. We extend this to a larger class of Gaussian processes. |
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Keywords: | Itô formula Skorohod integral Malliavin calculus Fractional Brownian motion |
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