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A counter example to central limit theorem in Hilbert spaces under a strong mixing condition

   
@article{ECP3249,
	author = {Davide Giraudo and Dalibor Volny},
	title = {A counter example to central limit theorem in Hilbert spaces under a strong mixing condition},
	journal = {Electron. Commun. Probab.},
	fjournal = {Electronic Communications in Probability},
	volume = {19},
	year = {2014},
	keywords = {Central limit theorem, Hilbert space, mixing conditions,  strictly stationary process},
	abstract = {We show that in a separable infinite dimensional Hilbert space, uniform integrability of the square of the norm of normalized partial sums of a strictly stationary sequence, together with a strong mixing condition, does not guarantee the central limit theorem.},
	pages = {no. 62, 1-12},
	issn = {1083-589X},
	doi = {10.1214/ECP.v19-3249},    
        url = {http://ecp.ejpecp.org/article/view/3249}}