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We investigate the invariance principle in H{\"o}lder spaces for strictlystationary martingale difference sequences. In particular, we show that thesufficient condition on the tail in the i.i.d. case does not extend tostationary ergodic martingale differences. We provide a sufficient condition onthe conditional variance which guarantee the invariance principle in H{\"o}lderspaces. We then deduce a condition in the spirit of Hannan one.

Holderian weak invariance principle under a Hannan type condition