Open AccessA maximal 𝕃_{𝕡}-inequality for stationary sequences and its applications
Author(s) -
Magda Peligrad,
Sergey Utev,
Wei Biao Wu
Publication year - 2006
Publication title -
proceedings of the american mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.968
H-Index - 84
eISSN - 1088-6826
pISSN - 0002-9939
DOI - 10.1090/s0002-9939-06-08488-7
Subject(s) - annotation , bounded function , algorithm , mathematics , type (biology) , martingale (probability theory) , computer science , artificial intelligence , mathematical analysis , ecology , biology
The paper aims to establish a new sharp Burkholder-type maximal inequality in L p \mathbb {L}_p for a class of stationary sequences that includes martingale sequences, mixingales and other dependent structures. The case when the variables are bounded is also addressed, leading to an exponential inequality for a maximum of partial sums. As an application we present an invariance principle for partial sums of certain maps of Bernoulli shifts processes.