Let X be a random variable with values on the (classical) Wiener space whose law is absolutely continuous w.r.t. the reference Wiener measure (and satisfying a proper notion of "mean zero" and "unit variance"). Let X_1,...X_n be i.i.d. copies of X. Does the density (w.r.t the Wiener measure) of (X_1+...+X_n)/ \sqrt{n} converge in L^1 to 1?
Sulaiman Sani
The Donsker Theorem is a limit theorem for a sequence of stochastic process. It is also easily applicable.
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Alberto Lanconelli
As far as I know, Donsker Theorem is about convergence in distribution, isn't it?
I am looking for a result on the L^1-convergence of the densities.
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Alberto Lanconelli
Dear George,
I am one of the authors of the paper from the link.
Thank you for your interest in my question.
Best wishes,
Alberto
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