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Abstract: We compute explicit bounds in the normal and chi-square approximations ofmultilinear homogenous sums of arbitrary order of general centeredindependent random variables with unit variance. In particular, we show thatchaotic random variables enjoy the following form of universality: a thenormal and chi-square approximations of any homogenous sum can be completelycharacterized and assessed by first switching to its Wiener chaos counterpart,and b the simple upper bounds and convergence criteria available on theWiener chaos extend almost verbatim to the class of homogeneous sums.



Author: Ivan Nourdin, Giovanni Peccati, Gesine Reinert

Source: https://arxiv.org/







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