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

Davide Giraudo (1) , Dalibor Volný (1)

1 LMRS - Laboratoire de Mathématiques Raphaël Salem

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.

Domaines: Probabilités [math.PR]

Davide Giraudo, Dalibor Volný. A counter example to central limit theorem in Hilbert spaces under a strong mixing condition. Electronic Communications in Probability, 2014, 19 (62), pp.1-12. ⟨10.1214/ECP.v19-3249⟩. ⟨hal-00926949⟩