Holderian weak invariance principle under a Hannan type condition

Davide Giraudo (1)

1 LMRS - Laboratoire de Mathématiques Raphaël Salem

We investigate the invariance principle in Hölder 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 Hölder spaces. We then deduce a condition in the spirit of Hannan one.

Domaines: Probabilités [math.PR]

Davide Giraudo. Holderian weak invariance principle under a Hannan type condition. Stochastic Processes and their Applications, 2016, 126, ⟨10.1016/j.spa.2015.09.001⟩. ⟨hal-01128232v2⟩