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Holderian weak invariance principle under a Hannan type condition

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  • Giraudo, Davide

Abstract

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.

Suggested Citation

  • Giraudo, Davide, 2016. "Holderian weak invariance principle under a Hannan type condition," Stochastic Processes and their Applications, Elsevier, vol. 126(1), pages 290-311.
    • Handle: RePEc:eee:spapps:v:126:y:2016:i:1:p:290-311
    DOI: 10.1016/j.spa.2015.09.001
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    References listed on IDEAS

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    1. Lesigne, Emmanuel & Volný, Dalibor, 2001. "Large deviations for martingales," Stochastic Processes and their Applications, Elsevier, vol. 96(1), pages 143-159, November.
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