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Asymptotic expansion for vector-valued sequences of random variables with focus on Wiener chaos

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  • Tudor, Ciprian A.
  • Yoshida, Nakahiro

Abstract

We develop the asymptotic expansion theory for vector-valued sequences (FN)N≥1 of random variables in terms of the convergence of the Stein–Malliavin matrix associated with the sequence FN. Our approach combines the classical Fourier approach and the recent Stein–Malliavin theory. We find the second order term of the asymptotic expansion of the density of FN and we illustrate our results by several examples.

Suggested Citation

  • Tudor, Ciprian A. & Yoshida, Nakahiro, 2019. "Asymptotic expansion for vector-valued sequences of random variables with focus on Wiener chaos," Stochastic Processes and their Applications, Elsevier, vol. 129(9), pages 3499-3526.
    • Handle: RePEc:eee:spapps:v:129:y:2019:i:9:p:3499-3526
    DOI: 10.1016/j.spa.2018.09.018
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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. Yoshida, Nakahiro, 2013. "Martingale expansion in mixed normal limit," Stochastic Processes and their Applications, Elsevier, vol. 123(3), pages 887-933.
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    Cited by:

    1. Yoshida, Nakahiro, 2023. "Asymptotic expansion and estimates of Wiener functionals," Stochastic Processes and their Applications, Elsevier, vol. 157(C), pages 176-248.
    2. Tudor, Ciprian A. & Yoshida, Nakahiro, 2023. "High order asymptotic expansion for Wiener functionals," Stochastic Processes and their Applications, Elsevier, vol. 164(C), pages 443-492.

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