High order asymptotic expansion for Wiener functionals

Ciprian Tudor (1) , Nakahiro Yoshida (2)

1 LPP - Laboratoire Paul Painlevé - UMR 8524
2 Graduate school of mathematics

By combining the Malliavin calculus with Fourier techniques, we develop a high-order asymptotic expansion theory for a sequence of vector-valued random variables. Our asymptotic expansion formulas give the development of the characteristic functional and of the local density of the random vectors up to an arbitrary order. We analyzed in details an example related to the wave equation with space-time white noise which also provides interesting facts on the correlation structure of the solution to this equation.

Mots clés: and Phrases: Asymptotic expansion; Stein-Malliavin calculus; Central limit theorem; cumulants; wave equation

Domaines: Probabilités [math.PR]

Ciprian Tudor, Nakahiro Yoshida. High order asymptotic expansion for Wiener functionals. 2019. ⟨hal-02291565⟩