Title :

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

Author(s) :

Tudor, Ciprian [Auteur]
Laboratoire Paul Painlevé - UMR 8524 [LPP]
Yoshida, Nakahiro [Auteur]

English keyword(s) :

and Phrases: Asymptotic expansion
Stein-Malliavin calculus
Quadratic variation
Fractional Brownian motion
Central limit theorem
Fourth Moment Theorem

HAL domain(s) :

Mathématiques [math]/Probabilités [math.PR]

English abstract : [en]

We develop the asymptotic expansion theory for vector-valued sequences (F N) N ≥1 of random variables in terms of the convergence of the Stein-Malliavin matrix associated to the sequence F N. Our approach combines the ...
Show more >We develop the asymptotic expansion theory for vector-valued sequences (F N) N ≥1 of random variables in terms of the convergence of the Stein-Malliavin 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, 62H12Show less >

Language :

Anglais

Collections :

• Laboratoire Paul Painlevé - UMR 8524

Source :

Harvested from HAL