Convergence Towards Linear Combinations of Chi-Squared Random Variables: A Malliavin-Based Approach

@inproceedings{Azmoodeh2014ConvergenceTL,
  title={Convergence Towards Linear Combinations of Chi-Squared Random Variables: A Malliavin-Based Approach},
  author={E. Azmoodeh and G. Peccati and Guillaume Poly},
  year={2014}
}
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 \(\Gamma _{i}\) (introduced by Nourdin and Peccati, J. Appl. Funct. Anal. 258(11), 3775–3791, 2010), we provide conditions that apply to random… Expand
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