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New Central Limit Theorems for Functionals of Gaussian Processes and their Applications

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  • José Manuel Corcuera

    (Universitat de Barcelona)

Abstract

As a consequence of the seminal work of Nualart and Peccati in 2005 we have new central limit theorems for functional of Gaussian processes that have allowed us to elucidate the asymptotic behavior of the multipower variation of certain ambit processes, see Barndorff-Nielsen et al. (2009c). This survey intends to explain the role of the Malliavin calculus to reach these results.

Suggested Citation

  • José Manuel Corcuera, 2012. "New Central Limit Theorems for Functionals of Gaussian Processes and their Applications," Methodology and Computing in Applied Probability, Springer, vol. 14(3), pages 477-500, September.
    • Handle: RePEc:spr:metcap:v:14:y:2012:i:3:d:10.1007_s11009-011-9236-9
    DOI: 10.1007/s11009-011-9236-9
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    References listed on IDEAS

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    1. Breuer, Péter & Major, Péter, 1983. "Central limit theorems for non-linear functionals of Gaussian fields," Journal of Multivariate Analysis, Elsevier, vol. 13(3), pages 425-441, September.
    2. Ole E. Barndorff-Nielsen & José Manuel Corcuera & Mark Podolskij, 2009. "Multipower Variation for Brownian Semistationary Processes," CREATES Research Papers 2009-21, Department of Economics and Business Economics, Aarhus University.
    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.
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