Holderian weak invariance principle for stationary mixing sequences

Davide Giraudo (1)

1 LMRS - Laboratoire de Mathématiques Raphaël Salem

We provide some sufficient mixing conditions on a strictly stationary sequence in order to guarantee the weak invariance principle in H\"{o}lder spaces. Strong mixing, $\rho$-mixing and interlaced $\rho$-mixing conditions are investigated as well as $\tau$-dependent sequences. The main tools are moment and Fuk-Nagaev type inequalities for mixing sequences and a truncation argument.

Domaines: Probabilités [math.PR]

Davide Giraudo. Holderian weak invariance principle for stationary mixing sequences. Journal of Theoretical Probability, 2015, pp.1-16. ⟨10.1007/s10959-015-0633-9⟩. ⟨hal-01075583v3⟩