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

Listed author(s):
  • Harnett, Daniel
  • Nualart, David
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    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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    Article provided by Elsevier in its journal Stochastic Processes and their Applications.

    Volume (Year): 122 (2012)
    Issue (Month): 10 ()
    Pages: 3460-3505

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    Handle: RePEc:eee:spapps:v:122:y:2012:i:10:p:3460-3505
    DOI: 10.1016/
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    1. 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.
    2. 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.
    3. 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.
    4. Russo, Francesco & Tudor, Ciprian A., 2006. "On bifractional Brownian motion," Stochastic Processes and their Applications, Elsevier, vol. 116(5), pages 830-856, May.
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