Weak convergence of the Stratonovich integral with respect to a class of Gaussian processes
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) . This formula was known for fBm with H=1/6 Nourdin et al. (2010) . We extend this to a larger class of Gaussian processes.
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Volume (Year): 122 (2012)
Issue (Month): 10 ()
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References listed on IDEAS
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- Nualart, D. & Ortiz-Latorre, S., 2008. "Central limit theorems for multiple stochastic integrals and Malliavin calculus," Stochastic Processes and their Applications, Elsevier, vol. 118(4), pages 614-628, April.
- Russo, Francesco & Tudor, Ciprian A., 2006. "On bifractional Brownian motion," Stochastic Processes and their Applications, Elsevier, vol. 116(5), pages 830-856, May.
- Bojdecki, Tomasz & Gorostiza, Luis G. & Talarczyk, Anna, 2004. "Sub-fractional Brownian motion and its relation to occupation times," Statistics & Probability Letters, Elsevier, vol. 69(4), pages 405-419, October.
- Lei, Pedro & Nualart, David, 2009. "A decomposition of the bifractional Brownian motion and some applications," Statistics & Probability Letters, Elsevier, vol. 79(5), pages 619-624, March.
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