Skip to Main content Skip to Navigation
Journal articles

INVARIANCE PRINCIPLES UNDER THE MAXWELL-WOODROOFE CONDITION IN BANACH SPACES

Abstract : We prove that, for (adapted) stationary processes, the so-called Maxwell-Woodroofe condition is sufficient for the law of the iterated logarithm and that it is optimal in some sense. That result actually holds in the context of Banach valued stationary processes, including the case of L-P-valued random variables, with 1 <= p < infinity. In this setting, we also prove the weak invariance principle, hence generalizing a result of Peligrad and Utev [Ann. Probab. 33 (2005) 798-815]. The proofs make use of a new maximal inequality and of approximation by martingales, for which some of our results are also new.
Document type :
Journal articles
Complete list of metadatas

https://hal-centralesupelec.archives-ouvertes.fr/hal-02404278
Contributor : Delphine Le Piolet <>
Submitted on : Wednesday, December 11, 2019 - 11:34:32 AM
Last modification on : Thursday, July 2, 2020 - 9:12:02 AM

Links full text

Identifiers

Citation

Christophe Cuny. INVARIANCE PRINCIPLES UNDER THE MAXWELL-WOODROOFE CONDITION IN BANACH SPACES. Annals of Probability, Institute of Mathematical Statistics, 2017, 45 (3), pp.1578-1611. ⟨10.1214/16-AOP1095⟩. ⟨hal-02404278⟩

Share

Metrics

Record views

30