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

Ciprian A. Tudor and Nakahiro Yoshida

Stochastic Processes and their Applications, 2019, vol. 129, issue 9, 3499-3526

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.

Keywords: Asymptotic expansion; Stein–Malliavin calculus; Quadratic variation; Fractional Brownian motion; Central limit theorem; Fourth moment theorem (search for similar items in EconPapers)
Date: 2019
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Citations: View citations in EconPapers (3)

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DOI: 10.1016/j.spa.2018.09.018

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