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 Weak convergence of the Stratonovich integral with respect to a class of Gaussian processes


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For a Gaussian process $X$ and smooth function $f$, we consider a Stratonovich integral of $fX$, 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 It\^o integral of $f-$ with respect to a Gaussian martingale independent of $X$. The proof uses Malliavin calculus and a central limit theorem from 10. This formula was known for fBm with $H=1-6$ 9. We extend this to a larger class of Gaussian processes.



Author: Daniel Harnett; David Nualart

Source: https://archive.org/







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