Abstract
We prove an asymptotic Cramér’s theorem, that is, if the sequence (X n + Y n ) n ≥ 1 converges in law to the standard normal distribution and for every n ≥ 1 the random variables X n and Y n are independent, then (X n ) n ≥ 1 and (Y n ) n ≥ 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.
- Multiple stochastic integrals
- Limit theorems
- Malliavin calculus
- Stein’s method
2000 AMS Classification Numbers: 60G15, 60H05, 60F05, 60H07
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We wish to thank the anonymous referee for valuable comments on our manuscript.
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Tudor, C.A. (2011). Asymptotic Cramér’s Theorem and Analysis on Wiener Space. In: Donati-Martin, C., Lejay, A., Rouault, A. (eds) Séminaire de Probabilités XLIII. Lecture Notes in Mathematics(), vol 2006. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-15217-7_12
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DOI: https://doi.org/10.1007/978-3-642-15217-7_12
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