Holderian weak invariance principle under a Hannan type condition

Abstract

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