Rosenthal-type inequalities for the maximum of partial sums of stationary processes and examples

Details Rosenthal-type inequalities for the maximum of partial sums of stationary processes and examples Rosenthal-type inequalities for the maximum of partial sums of stationary processes and examples

2011-03-16

arxiv.org/abs/1103.3242v1

Mathematics

Probability

Scientific paper

The aim of this paper is to propose new Rosenthal-type inequalities for higher moments of the maximum of partial sums of stationary sequences including martingales and their generalizations. As in the recent results by Peligrad et al. (2007) and Rio (2009), the estimates of the moments are expressed in terms of the norms of projections of partial sums. The proofs of the results are essentially based on a new maximal inequality generalizing the Doob's maximal inequality for martingales and dyadic induction. Various applications are also provided.

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