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

Daniel Harnett and David Nualart

Stochastic Processes and their Applications, 2012, vol. 122, issue 10, 3460-3505

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.

Keywords: Itô formula; Skorohod integral; Malliavin calculus; Fractional Brownian motion (search for similar items in EconPapers)
Date: 2012
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Citations: View citations in EconPapers (3)

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DOI: 10.1016/j.spa.2012.06.008

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