Asymptotic expansion for vectorvalued sequences of random variables with focus on Wiener chaos
Abstract
We develop the asymptotic expansion theory for vectorvalued sequences (F N) N $\ge$1 of random variables in terms of the convergence of the SteinMalliavin matrix associated to the sequence F N. Our approach combines the classical Fourier approach and the recent theory on Stein method and Malliavin calculus. We find the second order term of the asymptotic expansion of the density of F N and we illustrate our results by several examples. 2010 AMS Classification Numbers: 62M09, 60F05, 62H12
 Publication:

arXiv eprints
 Pub Date:
 December 2017
 DOI:
 10.48550/arXiv.1712.03123
 arXiv:
 arXiv:1712.03123
 Bibcode:
 2017arXiv171203123T
 Keywords:

 Mathematics  Probability