Asymptotic Cramér's theorem and analysis on Wiener space

Details Asymptotic Cramér's theorem and analysis on Wiener space Asymptotic Cramér's theorem and analysis on Wiener space

2010-06-20

arxiv.org/abs/1006.3922v1

Mathematics

Probability

To appear in "Seminaire de Probabilites XLIII"

Scientific paper

We prove an asymptotic Cram\'er's theorem, that is, if the sequence $(X_{n}+ Y_{n})_{n\geq 1}$ converges in law to the standard normal distribution and for every $n\geq 1$ the random variables $X_{n}$ and $Y_{n}$ are independent, then $(X_{n})_{n\geq 1}$ {\it and } $(Y_{n}) _{n\geq 1}$ converge in law to a normal distribution. Then we compare this result with recent criteria for the central convergence obtained in terms of Malliavin derivatives.

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