2014/09/19 by Ehsan Azmoodeh, Azmoodeh, Ehsan, Giovanni Peccati +3
Economics, Econometrics and Finance · Mathematics · #FOS: Mathematics #Mathematical Dynamics and Fractals #Probability (math.PR) #Stochastic processes and financial applications #Stochastic processes and statistical mechanics
paper · doi:10.48550/arxiv.1409.5551
openalex publication_date 2014/09/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We investigate the problem of finding necessary and sufficient conditions for convergence in distribution towards a general finite linear combination of independent chi-squared random variables, within the framework of random objects living on a fixed Gaussian space. Using a recent representation of cumulants in terms of the Malliavin calculus operators Γi (introduced by Nourdin and Peccati in \citen-pe-3), we provide conditions that apply to random variables living in a finite sum of Wiener chaoses. As an important by-product of our analysis, we shall derive a new proof and a new interpretation of a recent finding by Nourdin and Poly \citen-po-1, concerning the limiting behaviour of random variables living in a Wiener chaos of order two. Our analysis contributes to a fertile line of research, that originates from questions raised by Marc Yor, in the framework of limit theorems for non-linear functionals of Brownian local times.